I'm going to cut off my good friend of 3 years, who has admitted his romantic feelings for me, because I've started seeing someone
How do you feel about seeing him as a friend now? Is there any other reason why you feel the need to cut off your friend?
No, I feel indifferent, I don't care about him anymore.
It's okay if you to only want to have one romantic interest at a time, but you shouldn't cut off your friend entirely. You can have your personal boundaries, and just tell your friend that you are not interested in romance, whether or not you are currently seeing someone else.
Why would I do that when I've already rejected him and keep him at arm's length?
If isn't still trying to have a romantic relationship with you, then I think it would be rude to just cut him off. I'm sure the person you're seeing would understand, and you seem to have already set boundaries with him.