"Karma" is from Buddhism and Hinduism. It is usually used to describe how your past actions create your fate (in Buddhism and Hinduism, this can also mean how your past lives can affect the fate of your current life).
"Karma" is also used as slang in the U.S. - the meaning is similar but it is not religious or spiritual. So the lyrics, "Let's not kill the karma, let's not start a fight," are a request to avoid bad/wrong actions ("a fight") because it will cause "bad karma" (a bad fate).
To be honest, their use of this word is not very good or correct. I think they liked that it kind of rhymed with "drama" in the next song lyric. :-) It makes sense but it's not the common way that English speakers use the word, even as slang. A more common slang sentence would be something like "You're going to get good karma points for bringing homemade soup to the elderly neighbor," or "Don't try to cheat the customers at your store - it's bad karma!"
I hope this helps!