I am having trouble killing targets without being caught as a magic user. They do not go down in one hit. Anything I can do??

Quiet Casting perk? Makes all spells silent to NPCs. You will need at least a 50 in Illusion plus you must take the Novice Illusion, Animage, and Kindred Mage perks first.

Edit: altho TBH I don't know how well it works if you still don't kill them in one hit. Seems like someone who just got blasted with a destruction spell would tend to notice once it hit them. Might not give away your position, though, if you stay hidden and have a high enough sneak skill, they might look for you but give up if they can't find you.

You could also try using a paralyze spell which, I think, would make it so you could get multiple casts off on your target without allowing him to scream for help.