Instructions
End the mission by killing off your character. When you come back to life, the mission you were on will be cancelled and you'll be able to start another mission.
Start a new game. This will cancel the mission you're on and disable any cheat codes you've entered.
Allow yourself to get arrested during a mission, which will end the mission you're on.
Wait for the mission to end on its own, if it's a timed mission. Some missions are time-sensitive. These missions will end if you don't complete them in the allotted time frame.