I'm going to cancel a friend's invite to a birthday party
That's not very nice. Why are you cancelling your friend's invite?
I don't see the point of inviting them to the party.
If you do not want some people to go to your party then you should not have invited them in the first place. Inviting people to a party gives expectations to people and if you cancel them, it makes them feel bad and their expectations are ruined. You might feel bad when you find out how hurt their feelings get.
Most people can get over it and I don't feel bad in doing it.
I really think you should reconsider uninviting a friend to the party. Think of how you would feel if your friend excluded you like that.