Hi, I am trying to reset a local server of a game which saves its game save files where BYOND keeps them and I don't know where that is to delete. Can someone point me in the right direction?

BYOND Version 513.1539
First off, you should update your BYOND; 513 is a full major version behind.

The savefiles are stored in the same directory as the game files, or a subdirectory thereof. Usually games will use a subdirectory like saves/ to store the files. The exact choice of where and how to store save info varies by game, but it has to be under the game's own directory somewhere.

So you'd want to go to your BYOND user data directory (usually Documents\BYOND), and open up the MyHub folder. Then look for the author of the game, then the game itself. There you'll find the game's files. Somewhere in there you'll find the savefiles.