Beginner Gardening: Teach me to save this Cactus, 1 by NoobNewbie

NoobNewbie wrote:
Hello, Im both new to the forum and well, plants.
First off, I got this cactus and I wanna know if it\'s doing ok. And if it isnt, how serious is its condition. From what Ive been reading I think it\'s a mammillaria (not sure if it\'s zeilmanniana or spinosissima though), and of course it\'s obvious I have some cutting to do in order to let it grow healthily but I just wanna make sure if cutting is the only thing I would need to do. Im not sure if a picture is enough to determine its condition but any insights would be greatly appreciated.

As for the cutting bit, Ive been reading through a few sites on cactus care and they mentioned how Im supposed to cut at a 45 degree angle but Im still very nervous that I might harm prickly by accident. Also I read that I should try to get some roots when removing the offshoot but I think the pups are attached to the main body rather than at the base @@
I was hoping the picture attached would grant me with even more specific directions perhaps?

Thank you for your time!