You don't have to do that, especially for minis. The "5-leaflet leaf set" thing is primarily for hybrid teas to get longer stems. Basic deadheading is removing the bloom only. The plant will send out new growth that should end in a bud, and you can remove any old cane that dies off.

But, over pruning shouldn't have caused yellowing leaves. Is the plant inside or outside? If inside, then it isn't getting enough sunlight, roses want to be planted outside. If outside, then it might be over or under watered.

Oh, its outside. But I haven't changed its amount of water recently :(. I may have trimmed it back too much then > W >

It sounds like you're mini might be getting black spot. Most mini's get it if not sprayed with a fungacide. About where do you live?? Location makes a big difference.