The answer to this question can be found in Act II scene 1 of this excellent tragedy. The conspirators are gathered together, and they are working out a list of those who need to be killed in order to ensure that their assassination of Caesar and the usurpation of power is successful. It is Cassius who suggests that Antony should not "outlive Caesar," and suggests, quite accurately as it turns out, that he would be a "shrewd contriver" who could act against them. It is thus that he argues that the conspirators should "Let Antony and Caesar fall together."
However, Brutus argues against this, saying that to kill Antony in addition to Caesar would be equivalent to cutting the head off a corpse and then hacking the limbs. He says that Mark Antony is "but a limb of Caesar" and thus once Caesar himself is killed will be harmless:
And for Mark Antony, think not of him;
For he can do no more than Caesar's arm
When Caesar's head is off.