When you change the timeline, people disappear and are replaced by their new selves. This is what happens at the beginning of the movie. Vala, Teal'c, etc. disappear, while Mitchell, Sam and Daniel don't because they in the stargate's temporal vortex when their turn came.
But then why didn't Alternate Mitchell disappear after he killed Ba'al on the Achilles? Shouldn't he have disappeared since a new Mitchell went on to be born and the Tok'ra extraction ceremony went on normally?