I am relatively new to HBD and trying to figure out when to cut players that are not worhty of promoting. When do you cut your Rookie Level players, so you are not paying their salary the following year and can fill your Rookie roster with drafted players?

Rather than cutting them, you should be promoting them to Low A.  And promote Low A guys to AA, etc.  Your only cuts should be coming at either AA or AAA.

And to specifically answer your question, I do all my promotions and/or releases after the end of the minor league season, or after my teams get eliminated from the minor league playoffs.

I just keep track of, and promote, the guys that I think should go up a level.  Even if I don't expect them to ever make the bigs they still go up should they deserve it.  All the others I leave where they are until they get smart and retire on me.  They are filler in the minor leagues.  Sometimes a certain minor leaguer gets on my nerves for some reason if I'm paying attention and then I try to cut him and send him packing right when I think it will hurt the most.

Retirement of minor leaguers due to non-promotion is the biggest contributor to the total lack of minor league free agents in many worlds.

i fill my minor league rosters from AAA down to Low A, including extra inactives, at the start of the season.  Anyone that doesnt make a roster gets stored in Rookie.  After the draft, I set my RL roster and then will look to see what inactive spots I have left at higher levels and toss a few leftover guys that didnt make my RL roster there.  Anyone still leftover gets cut then.  As I result, I rarely cut anyone and instead just find inactive roster spots for them in the lower minor leagues....who knows, I may need that guy as an extra body to fill a roster out next season if minor league retirements hit me hard.

Thank you. Very helpful.