How do you know Mark was written 'after' the year 70?
While in Rome Mark wrote mostly for the Romans either during the first or second imprisonment of Paul.
Mark joined Paul in sending greetings to the Colossian Christians- Col 4v10
and greetings to Philemon -vs 23,24.
While still in prision Paul asked Timothy to bring Mark. -2nd Tim 4v11.
Mark [as Peter's spiritual son] was also in association with Peter in Babylon sending greetings.
1st Peter 5v13.
most biblical scholars agree mark was written 65-80
"Irenaeus wrote (Against Heresies 3.1.1): "After their departure [of Peter and Paul from earth], Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter." Note that Irenaeus had read Papias, and thus Irenaeus doesn't provide any independent confirmation of the statement made by the earlier author...."
Gospel of Mark
i recommend this too
FRONTLINE: from jesus to christ - the first christians: watch the full program online | PBS
if you want to read more from the 1st link...
"Nevertheless, even though the author may have been a disciple of Peter at some point, the author of the Gospel of Mark needn't have limited himself to Peter's preaching for his material. The NAB introduction says: "Petrine influence should not, however, be exaggerated. The evangelist has put together various oral and possibly written sources--miracle stories, parables, sayings, stories of controversies, and the passion--so as to speak of the crucified Messiah for Mark's own day."
"John P. Meier provides an example in which the author of Mark shows himself to be dependent on oral tradition. The story of the feeding of the multitude is found twice in Mark and once in John. Meier writes (A Marginal Jew, v. 2, pp. 965-6): "This suggests a long and complicated tradition history reaching back to the early days of the first Christian generation. Prior to Mark's Gospel there seems to have been two cycles of traditions about Jesus' ministry in Galilee, each one beginning with one version of the feeding miracle (Mk 6:32-44 and Mk 8:1-10). Before these cycles were created, the two versions of the feeding would have circulated as independent units, the first version attracting to itself the story of Jesus' walking on the water (a development also witnessed in John 6), while the second version did not receive such an elaboration. Behind all three versions of the miracle story would have stood some primitive form."
"The author of the Gospel of Mark does indeed seem to lack first-hand knowledge of the geography of Palestine. Randel Helms writes concerning Mark 11:1 (Who Wrote the Gospels?, p. 6): "Anyone approaching Jerusalem from Jericho would come first to Bethany and then Bethphage, not the reverse. This is one of several passages showing that Mark knew little about Palestine; we must assume, Dennis Nineham argues, that 'Mark did not know the relative positions of these two villages on the Jericho road' (1963, 294-295). Indeed, Mark knew so little about the area that he described Jesus going from Tyrian territory 'by way of Sidon to the Sea of Galilee through the territory of the Ten Towns' (Mark 7:31); this is similar to saying that one goes from London to Paris by way of Edinburgh and Rome. The simplist solution, says Nineham, is that 'the evangelist was not directly acquainted with Palestine' (40)."
The destruction of the Temple, which happened in 70 CE, is mentioned in v. 1-4. Leaving the temple area, a disciple said: "Teacher, look at the huge blocks of stone and the enormous buildings!" Facing the temple, Jesus responds: "You see these great buildings? Not one stone will be left upon another - all will be torn down." Peter and some others then question Jesus about the signs of the apocalypse privately, a tell-tale sign of Mark's redactional hand (instead of earlier well-known tradition).
In v. 5-8, the author speaks of "wars and rumours of wars," but "this is not yet the end." If ch 13 is speaking of the First Jewish Revolt, this indicates that some had predicted earlier that the end would come during the war, a view which the author must deny (or perhaps slightly modify, cf v. 24) after the fighting has ended. The author speaks of "famine" during this time when nation is rising against nation, and Josephus reports the horrors of pestilence and famine during the First Jewish Revolt.
Concerning v. 9-13, Robert Funk writes in The Five Gospels: "The sayings in Mark 13:9-13 all reflect detailed knowledge of events that took place - or ideas that were current - after Jesus' death: trials and persecutions of Jesus' followers, the call to preach the gospel to all nations, advice to offer spontaneous testimony, and the prediction that families would turn against one another are features of later Christian existence, not of events in Galilee or Jerusalem during Jesus' lifetime. The note about children betraying their parents may be an allusion to the terrible calamities that took place during the siege of Jerusalem (66-70 C.E.)"
Verse 14 says: "When you see the 'Abomination of Desecration' standing where it should not be - let the reader take note! - those in Judea must flee to the mountains." The parenthetical comment to "let the reader take note" underscores the fact that this speech was written for the Christians of Mark's time. The contemporary audience of Mark would understand very well what he was talking about, although the 'Abomination of Desecration' is a cryptic reference to us. The phrase is borrowed from Dn 9:27, where it refers to Antiochus profaning the Temple of Jerusalem c. 165 BCE (probably with an image of Zeus), although it has been adapted to the evangelist's times. In the context of the First Jewish Revolt, this probably refers to the profanation of the Temple by the Romans. Josephus tells us that the victorious soldiers raised their imperial standards and worshiped them in the holy place (Wars of the Jews 6.6.1).
Randel Helms comments on the reference to Daniel in the Gospel of Mark (op. cit., p. 8):
So Daniel's "time, times, and half a time" is three and a half years, or twelve hundred and ninety days. The author of Daniel was referring, with the "abomination of desolation," to the altar to Zeus that Antiochus IV established in the Jerusalem temple in December, 167 B.C.E., as I Maccabees 1:54 tells us. But in Mark's eyes, Daniel really was speaking of Mark's own time, the "time of the end," when another "abomination of desolation" was set up in the Jerusalem temple. For according to Josephus, the regular offering ceased in the temple in July, 70, the temple was burnt in August, and later that month the imperial Roman eagle was set up in the temple precincts and sacrifice was offered to it; then in September the temple was razed to the ground (Josphus, The Jewish War, Chapters 6, 7). Three and a half years thereafter would be early in the year 74. It should not be surprising that a first-century author might apply the Book of Daniel to the Jewish War; Josephus himself did so, he tells us, in the summer of the year 70, at the height of the seige (Josephus, 309).
Helms goes on to argue that the reference to the messianic pretenders in 13:21-22 suggests that the author of Mark wrote shortly after 70 rather than a few years before. Josephus tells us about Menahem, the son of Judas, as well as Simon, the son of Gioras, "both of whom were striking messianic pretenders." Helms states, "As far as Mark was concerned the Jewish War was over; there remained only the cosmic disorder and the Second Coming."