Mating Between Consenting Adults
1. The rooster dances to show his intentions. He lowers a wing and sort of sidesteps around the hen.
2. The hen squats. This gets her body on the ground so the rooster's weight goes into the ground through her body instead of just her legs. Most roosters of the same breed as the hen are heavier than the hen so the squat is nature's way of protecting her legs and joints.
3. The rooster hops on and grabs the back of her head. This head grab helps line him up right and helps him keep his balance, but the main purpose is to tell her to raise her tail up out of the way so he can hit the target. Without the head grab he would not be able to get to the target so there would be no fertile eggs.
4. The rooster touches her vent with his. That deposits the sperm. This may take a couple of seconds or may be over in a flash.
5. The rooster hops off, his part is done. The hen stands up, fluffs up her feathers, and shakes. This fluffy shake gets the sperm in a special container where it can stay viable from a week to maybe three weeks.
It doesn't always go this way between adults. Sometimes the rooster does not dance but just grabs and hops on. No harm no foul, but it shows he does not have the self-confidence he should. Sometimes the hen runs away instead of squatting. The rooster may let her go or he may give chase. If he chases the hen may squat, she just wanted to know he was serious. He may stop the chase pretty quickly and let her go. He may chase her down and force her. As long as she squats and is not injured it's all OK. Even when he forces her it is usually not very violent.
I wasn't sure whether to post that above or not but I thought it might be beneficial. It might help explain some of what you are seeing, especially the gripping. Not all adults are consenting. Hens often expect a rooster to display certain traits that show he will be a good father of their children. Not all adult males can do that. Not many immature cockerels can and it sounds like yours is still young. Size isn't everything, maturity is more important. Some hens are so strong-willed they will not submit to a male. This can get violent, especially when a make is going through puberty. Sometimes the hen can be the brutal one. Not all males meet our definition of "nice" but neither do all hens. Each individual has their own personality and each flock has it's own dynamics which can change when you add or subtract an individual. And no, I do not believe breed has anything to do with it.
my current rooster is the son and he has just matured to full size and has started mating.
I feel like this caveman of a rooster is going about raising the stress levels of my flock.
He very well could be. If he is still immature (and it sounds like he could be) there is a reasonable chance he will mature out of this stage and the girls will accept him when he matures. If you get rid of him and raise another immature male with your flock you will possibly (or maybe even probably) see the same behaviors as the new one goes through puberty. It is pretty common behavior. If he were fully mature and this was going on it would be time to get another one if you really want a rooster. If the pullets or hens are really getting injured it would be a good time to separate the male.