Can I refuse a stipend during a PhD program? I was admitted to a US PhD program (in computer science, if that matters) with fellowship + stipend.

I am getting a separate stipend from my government (which is higher than the university stipend), but they forbid me from getting an additional stipend from the university.

Is it OK to ask the university to just pay for my tuition (with the fellowship), and refuse the stipend?
Yes. The university will generally be happy to work with you to make sure your tuition is covered and call the money whatever they need to. As you are saving the department money, you may also ask the department to provide some additional travel or research funds instead of the stipend.