You cite two goals in the comments:
My goals are 1.) avoid engaging in uncomfortable discussion of topic and 2.) reduce frequency of comments
I think that your two goals oppose each other.
If you avoid engaging, then you risk their not learning that you don't appreciate their comments, and they may very well just keep making them.
Your desire to avoid offending is admirable, but they're your SO. There are times in your relationships (especially in close ones) where you will need to have uncomfortable conversations.
Like you say:
I don't think that's a good approach to use with someone I'm supposed to have good communication with.
Don't avoid these uncomfortable conversations, because then you will end up putting up with things that you don't want to put up with.
Tolerating leads to resenting.
This is supposed to be the person that you may spend the rest of your life with. If you have a problem with their behavior, you should bring it up to them. Yes, it may be uncomfortable, but you need to do it for your relationship.
You have several options.
If the joke is simply unfunny, but not particularly offensive, you don't need to make a big deal about it. You could just not laugh and let it go, or ask what's funny about it. Over time, your SO may adapt to your sense of humor.
If you find your SO's jokes offensive though, you may take a different approach.
Not laughing or asking what's so funny about it is an option (though it contradicts my point above about communicating with your SO). It is certainly possible that your SO will adapt to your sense of humor and stop.
If your SO doesn't though, which seems to be the case given what you stated, then just stop them after the joke and directly, but calmly state:
Sorry, but I don't find those types of jokes funny, and in fact find them a bit offensive.
(You can then clarify what you find offensive about it if you want)
Then, the ball is in their court.
If they apologize and don't make jokes like that again, then mission accomplished.
If they do, then bring it up again, but this time cite their past jokes as backup:
Hey, look you've made jokes like this before (1, 2, 3, etc.), but I just don't find that type of humor funny (because...)
Again, don't lose your cool and take it out on your partner, and focus on the fact that you don't find it funny rather than they're not funny. Prefer I'm offended to you're offensive.
Then, again, the ball is in their court.
The thing is, you can't really change people, or at least you can't expect them to change.
You cannot force your SO to have a different sense of humor.
They may choose to compromise and avoid jokes that offend you (which is obviously a win for you), or they may chose to not compromise and do what they want. If that's their choice, then you have to decide for yourself, how important is it that they don't make jokes like that.
Is this something that's worth breaking up over? If yes, then break up.
If it's not, then you might have to compromise and allow them to make jokes like that. It's not ideal, but it's sometimes how these things go.
But at least you'd have brought it up and not let resentment build inside of you.