Firstly, one of the methods to deal with the overhand punch is by leaning or stepping back just enough so that the punch misses your face. When your opponent throws their right punch, they become open to the right side of their face, making a jab cross, or hook cross combination a perfect counter to this attack. After you dodge the punch, you want to try and land an attack of your own. If you do not counter, your opponent may continue to swing and build off their momentum. You can see this in action at the 1:29 mark of my video.
The second way of dealing with the overhand punch is to block it using the 360 block. Almost straighten your lead arm so that it is at a 160 degree angle (almost straight) and angle it out to your left at a 45 degree angle. Because the overhand punch is thrown in a circular motion, your opponent’s punch will run into your lead arm and get blocked. As the punch comes, you can also wrap your lead arm onto your opponent’s bicep or arm as he throws the overhand punch to tie up with him. At this point, you have the option to throw short hooks and uppercuts, continue the fight grappling, or disengage by pushing off. This strategy is actually how Daniel Cormier became double champion against Stipe Miocic.
The third option is to time a left roundhouse kick to the body as soon as you see the big right punch coming. When throwing the big right punch, the right side of your body is left wide open for a counter which Muay Thai champ, Buakwaw, uses frequently.
The final method to overcome the overhand punch is shooting for a takedown. The overhand punch is usually thrown with power, and to generate power, you usually need to over commit with that right hand. As your opponent drives forward with the punch, you want to change levels to dodge the punch, and shoot right into the legs of your opponent, and drive them to the floor. Since their upper body is driving forward, by taking out the legs, you can easily take them to the ground.
I hope that you can practice these different methods next time you train or spar, and feel free to reach out to me if you have any questions.