When play with the salary cap penalties turned on in franchise mode, it is better to trade the player(s) you wish to cut for another team's draft pick. You will avoid penalties, keep your roster from becoming full, and get another draft pick.
Start a franchise and make a new coach (or make one under the Coach Option/Job Openings screen). In Coach Options/Job Openings screen, highlight your coach, then press Left or Right to select the team with the player or draft pick you want. You are now the coach of that team. Trade the player you want to your team, then return to the Job Openings screen in Coach Options and select your original team. Back out and you will be coaching your team again.
Start a franchise and choose all 32 teams. Also turn off the salary cap. Start the season, go to the roster, then trade a player. You will be able to trade with yourself without the rejection or the team. For example, you can trade Clinton Portis for Marshal Faulk, or Ed Macalfry for Terrell Owens.