Cole, who was limited in practice this week with a hamstring issue, is primarily a special-teams contributor. It's likely the team released Cole because he would not have been healthy enough to play this Sunday against Cincinnati.
By releasing Cole, the Patriots have reduced their active roster to 51 players. Given the time frame, promotions from the practice squad would seem likely to fill the final two spots.
The team has not yet signed a defensive tackle to replace Vince Wilfork, who was placed on injured reserve on Thursday. One scenario to fill Wilfork's spot would be to promote one of their practice-squad defensive tackles (A.J. Francis or Marcus Forston), while Cole's spot could once again go to rookie defensive back Kanorris Davis, who was promoted for last week's game before being waived again earlier this week.