Most towns have Babe Ruth, Junior American Legion, or some equivalent.
I would first try to set a time to speak with the coach and get some idea what you need to work on and some quick pointers from the coach on what he'd like to see during next year's tryout to give you the best chance to make the team. He will respect your passion, determination, and eagerness to improve.
If your arm is strong, mention the pitching, and he may grant you a tryout for that, but if you are not a top arm, he's not going to bring you on and take up a roster spot with a pitcher-only player.
If you get some information about why he cut you, I'm sure we can point you in the right direction on where to go for some good information. You will have to put in a lot of work, but if you really want to play, it's the only way to go.
There was a kid on my Varsity team who was an equipment manager as a Frosh and Sophomore. He made the team as a Junior and became a starter at 2B and team Captain his Senior Year.