A Mulligan, in a game, happens when a player gets a second chance to perform a certain move or action; usually due to lack of skill or bitter luck. A "Do-Over". Like getting an "Extra Play" in pinball due to sinking the ball before obtaining an arbitrary amount of points.
If your opening hand in Magic: The Gathering sucks bad; just call "Mulligan", reshuffle, and draw new cards.
When a dating relationship is brutally derailed by submerged emotional issues unknown to either person. If the derailer is allowed a second chance by the derailed, its a Mulligan. Even more so it accompanied by a decentbitch slap.