We mostly use this saying to express a deep level of strain. Whether on your personal time or physical body. So If you're working long hours, or if you have to wake up early for the gym. "I worked 70 hours last week and it's killing me because I hardly have time to enjoy the nice weather."

agree with the above - it can mean that the level of effort you are putting into something is killing you but it can also mean that you are waiting for something that you want so badly, and it's hard to wait. in this case it's sort of a shorter version of "the anticipation is killing me"....if someone is teasing me with something i can't have, i would say "you're killing me".