I also use a Dremel tool. I use those discs you use to cut metal. At least one member on here uses a Dremel grinder attachment to grind them down. Some people use dog nail clippers. I don't trust a potato so hot you can burn yourself or the chicken but some people use that method. Different people use different methods.
The spur and claws have a quick in them, sort of like your fingernails except it is inside where you can't see it. As long as you miss the quick it does not bleed or hurt. Unfortunately some quicks grow further up than others. With some roosters you may be able to take off half the spur and miss the quick. With others 1/4 may be the limit. I've never had serious bleeding when I hit the quick, maybe the cutting blade is hot enough to cauterize the wound, I don't know. And the rooster has never flinched or reacted when I hit the quick. However having a bit of flour or cornstarch available to toss on the wound and stop the bleeding would be a reasonable precaution. I've never had to but I've only done this a few times.
I wrap the rooster in a large towel around the wings and body. They are extremely calm when you do that but I hold onto the legs anyway. The towel or blanket needs to be big enough that it will not unwrap, you need your other hand to hold the legs to position them. I also clip off the point on their claws, just enough to blunt them. Those claws can be dangerous weapons.
When I'm finished I turn him loose with his flock. He usually immediately mates a hen to show it is still his flock, and things are then normal.