The first thing to understand about grooming a matted Poodle is that you can’t shave THROUGH mats - you must shave UNDER them. Mats tend to be close to the skin, so you need to carefully aim the clipper blade between the mats and your dog’s skin.
The safest blade to use on a matted Poodle is the #10 blade. With that being said, you can still injure your dog with this blade. Always be mindful of where your Poodle’s skin is.
If your Poodle is severely matted, the best thing to do is find a spot on your dog’s neck or back that isn’t matted where you can fit the clipper blade under the matting. Use short, gentle strokes to ease the mats off of your dog.
Don’t try to muscle the mats off with force - you’re more likely to cut your Poodle like that. Skin can be pulled up into mats, so you could be forcing the blade through skin instead of matted fur.
Use your spare hand to pull your Poodle’s skin taut to help prevent snagging loose skin in the clipper blade.
Go slow, take lots of breaks, and keep a first aid kit handy. Anybody (even professional groomers) can accidentally cut a dog. An inexperienced person shaving a matted dog is more likely to cut their dog than most.