I don't want to do that kind of thing with someone I'm not dating.
I don't get down like that.
I'm not that kind of girl/guy/person.
したくない= (I) don't want to do
こういうこと= that kind of thing; that sort of stuff
とは= with
付き合ってない人= someone I'm not dating; someone I'm not seeing; someone I'm not going out with.
一般的に言えば、"I don't do that kind of thing" または "I wouldn't do that sort of thing." といいます。
友達や家族と話しているとき、"I don't get down like that" (私だったら絶対しないことだけど) と"I'm not that kind of girl/guy/person"(私はそういうものなんかじゃないよ)もよく聞こえます。