In addition to what others already said:

• if you notice that you're angry / annoyed, don't act immediatly. Leave the PC, do something unrelated (like the dishes) for a few minutes and give yourself a little space to think about your next action. IMHO it is better to act / react a little later but with a calm mind and neutral language rather than giving in to anger and escalating the situation.

• If you're still angry, type a response anyway. Read it. Delete it. THEN write the actual response. Sometimes you have to let your anger out, but this doesn't mean that you have to send the message afterwards. Sometimes you need more than once "cycle" of venting-deleting-rewriting until the response is in an actual neutral tone, but it is worth the effort.

• Some people are simply trolls and only want to annoy / trigger others while pretending to be victims. Some people had a bad day and are unreasonably touchy, angry and frustrated, maybe a little drunk, and don't really notice that they're being assholes. It can be hard to distinguish between those two at first glance, but keep in mind that the comment history is public...

• If their other comments read a lot more calm and reasonable, I usually just ask whether they had a bad day and want to talk. Surprisingly, that does work more often than not to de-escalate a situation. You can also opt to just ask them to not do "it" again without immediatly resorting to mod tools, especially when the offense is something trivial like being off topic (just as a general rule, not related to your specific situation)
• However, if they behave like assholes all the time across all instances, or clearly show that they aren't interested in behaving like decent human beings even after a suspension/warning, then just block them. As a mod, you kinda have the responsibility to protect other users from nuisances, so this isn't exactly "powertripping", and the chances that the user in question suddenly starts to behave are slim. It's good to give people a second chance, but noone deserves a third chance unless they're showing effort to be better.

• Sometimes there is no "good" option. Sometimes you have to chose between "bad" and "worse" and it will feel bad.

As for your specific example, I'd tell them the following;

"That behaviour and attitude are not welcome here. You can chose to leave them at the doorstep when you enter this community, or you can stay out of the community along with the slurs. Your decision."