I've reported this many times through the game, but I figured I would report it here too.
There is a bug with the sniper weapons (as far as I can tell that's the only weapon this happens on) where, when using the sniping ability your character's animation gets stuck and you really can't do anything. You have to beam out then click "continue" to keep doing the mission.
It is very frustrating and seems to be happening more and more lately. I think this is something very important to look into and fix.
I've reported the bug many times myself. I haven't seen them mentioning it in their engineering reports so I'm not sure if they are even working on getting it fixed.
It can happen on all weapons.
Then you fire the second weapon ability and someone else kills your target, that is when you'll get stuck.
The last of all the bug reports I've filed about this problem is #854864. But I've filed a lot of them ever since Closed Beta. I wouldn't have a problem with it if the beam out and then continue mission solution didn't reset the mission progress.