Baseball Mogul gives you multiple ways to manage players in the last year of their contract (including those eligible for arbitration). The easiest way is to select "Expiring Contracts" in the Sortable Stats Dialog (on the Team Menu):
Then open the player's Scouting Report and click the "Negotiate" button:
However, if you still have expiring contracts at the end of the season, the game will force you to sign or release each of your players. This is frustrating, because you have to decide (for example) whether to sign Jon Lester before you know how much Felix Doubront is going to ask for in arbitration.
So ... we are adding a "Skip" button for Baseball Mogul Diamond.
It's a small feature, but for folks (like me) who wait until the end of the year to deal with expiring contracts, it makes it easier to keep your best players and still stay within your payroll budget.