Regarding What causes fur clumps on my cat's back, and how can I prevent them? , some severe cases of matted fur need to be removed through cutting or shaving.
As an electric shaver might spook a cat, are there any safety scissors that can be used?
What methods exist for an individual to perform a matted fur removal task safely?
When one of my past cats got old he started developing mats that I wanted to trim out (to keep them from getting worse). After once accidentally cutting him with the small scissors I was using (oops), I came up with the following solution:
I used a comb to comb from his skin to the mat. I then backed off (moved the comb toward his skin) just a bit, so that I could place the scissors between the comb and the mat. If the mat was far enough away from the skin I could cut it out that way; if not, I could still cut off part of the mat, which sometimes helped me comb the rest of it out.
My cat was old and docile so the fact that this required two hands (one or the comb and one for the scissors) wasn't a problem. If your cat resists combing, you would need a second person to hold/calm him.
A method I've used with some success is while petting the cat to gently tease the mat apart with my fingers until I have a gap I can guide snips through, then cut the mat open from the gap out.
I keep breaking the mat into progressively smaller pieces that can be either cut free or combed out, until it's gone. Sometimes this takes me several petting sessions with the cat (particularly the 18+ year old part Persian, part Siamese, and part who knows what with the long fluffy fur that periodically has fits of matting up really badly then will give me no problems for months on end).
A lot depends on the cat's temperament - if the cat is willing to sit and be petted and groomed you can do much more in a single session.
If the cat doesn't want to stay still for long, frequent short grooming sessions mixed with petting will help get the cat used to the idea that the brush or comb is not a bad thing, which in turn will make it easier to prevent mats as well as to get them out.
There are some lovely cat brushes, rubbery, comfy. Just lightly draw the brush not down but slowly across the matted fur a few times in order to get it lifting off the cat little by little.
Then brush down her back all over evenly, bit by bit to her tail, which my cat interprets as petting. You can use the hand you are not brushing with to maintain friendly contact. She purrs, though does not like the sides of her body done, so stop there.
Brush your own hair with the cat's brush. Show her the brush first. Show her the hairs after. Once the cat undetstands what is going on, she is compliant, and relieved to be cooler.
It is the extra-warm fluffy undercoat hair being shed. The coarse top coat is for year-round protection. In summer cats naturally shed their undercoat hair, and sometimes it mats up. If it is matted a lot, beyond brushing out, vets can help.
You may be able to use electric clippers; I've partially shaved 4 cats. All who got their first clip as adults. Clippers work best on mats that cover an extended area such as the whole way up a leg. It is still possible to damage the cat's skin with clippers. Take care doing the top front of the leg. 
my cat is not playing ball but I've tried to point where. There's a thin fold of skin that can fit between the teeth and easily be cut. I've also grazed a cat using clippers but I'm not 100% sure how.
You will almost certainly need a friend to hold the cat so you can access & see the mats. I recommend you do it in the bathroom, sat on the floor, as they are a small space and with the cupboards closed are lacking in hiding spaces. The easiest one to clip was the semi feral medium coat. Matted chest/ belly, armpits and back of leg. Under the circumstances I had to do it alone.
1 get everything you need in the room first. Comb, clippers, extension cord. If you are using a power point outside the room make sure it is turned on.
2 remove a mat and then let the cat go or pat/stroke them for a bit
3 if the cat really is not happy get a professional to do it
4 don't use clippers on a cat's head.
Once I had the first few mats off Kasie was willing to lie on my legs. The most difficult cat to clip was my friends Maine Coon cross who is super cuddly but complains and twists every time I try to scissor him.
Remember to brush/comb your cat daily after you have removed the mats to prevent new ones.
