Can't save money with the injury guarantee in place, and until he can pass a physical the guarantee will not go away.
To be the contrarian, Mayo's contract can indeed be re-structured if Mayo agrees. I would think that the $4.5M would need to continue to be guaranteed. If the $4.5M portion of the salary were moved to a bonus, $3M of 2015 cap money would be saved.
The risk to the team is minimal. If Mayo does not recover from injuries, the money is owed anyway. If Mayo is healthy, then the team will have he best LB corp in the NFL in addition to saving cap money.
Of course, this would give up on the dream of posters here to drastically cut Mayo's salary or be cut. That scenario could not be played out until June or so, after he has passed his physical. So, if the team wants to save the max, they will need to wait and cut Mayo. My personal view is the team has no interest in Mayo leaving.
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All this being said, if the team is willing to forego the immediate cap relief, they can wait until after Mayo's passes his physical June or even July and see how Mayo has progressed. At that point the team and Mayo can have a negotiation to decide how much Mayo might play for over the next three years. This re-write would be beneficial to the patriots in lots of ways, and also beneficial to Mayo.
Mayo probably SHOULD be paid less that $6.25M of new money. Waiting to negotiate would result in a pay cut; negotiating would likely not result in a pay cut, except perhaps a minor reduction in non-guaranteed money (perhaps $750K). Even that would reduce the cap reduction to $3.75M.
BOTTOM LINE
If Mayo is willing to reduce his salary by $750K and move $4.5M to a new bonus, then the team can say $3.75M in cap room.
So, Mayo could insist on keeping everything, but I suspect that he might agree to this $750K pay cut. Obviously, the $3M or $3.75M of cap room could be used to sign Gostkowski or Vereen or Ayers or Connolly and Casillas.