First off, the answer to this question is absolutely not.
For a solid reason backed by solid evidence, you can ask.
It is way too often that we see extremely insecure partners acting like they can control another person’s life.
And by the way, that is not OK.
See, your significant other is as much a human being as you are. They had their own friends and their own lives before you. Just because you walked into their life does not mean the world started revolving in the opposite direction. Their friends and family are an extension of them. They are what makes your significant other the person he / she is today.
Everyone gets jealous. Whether it’s an ex-girlfriend who stayed friends or just a friend who is very close to your significant other. We’ve all been there. But the key ingredient of a relationship is trust. If you don’t trust your significant other, then his / her friends are not the problem; it’s your relationship that needs to be resolved. Placing your insecurities of your relationship and reflecting them onto their friends is flat out wrong.
Telling your significant what to do is never OK. They are still their own person who has the right to make their own decisions. You can ask, sure. But developing unnecessary jealousy over someone who is of genuinely no threat to you and ordering your significant other to cut ties with them is not the appropriate way to approach this.
When you take away your partner’s free will, you’re being psycho. You are not thinking rationally, you are obsessing over your own insecurities you have about yourself and your relationship and reflecting them onto other people. Fix your trust issues. Work on your insecurities. Stop blaming everyone else. If you think removing another person in your partner’s life is going to solve your insecurities and trust issues, then you are very wrong.
Now, about asking, there are some circumstances where you can ask your significant other to reconsider a friendship. As I said before, cold, hard evidence is necessary. Say his / her friend is a deeply bad influence, or if someone made an inappropriate advancement toward your significant other and you have physical evidence, whether you saw it or have screenshots. Talking out these issues with your significant other is necessary. And, if they say no to your request, then you must try to understand that they have their own reasons behind it. Again, trust is the fundamental base of the relationship.
So next time you want to get all psycho about disliking your boyfriend’s friend who’s prettier and funnier than you, chill out because he loves you. And if he doesn’t, then you are young and you’ll find someone else.