He was cut because he was hurt. That is why
From the Newark Star Ledger (here in NY where I live):
Jets K Mike Nugent declined the team's contract offer and will test the open market.
The end of the Nuget!? Herm Edwards was rightly mocked for thinking the Jets were one kicker away from a title, spending a second-round pick on Nugent in 2005. They were rewarded with four mediocre seasons. Jay Feely, also a free agent, is expected to re-sign as the Jets kicker.
The Jets offered Nugent a competition for his job since Jay Feely who was older came in and outperformed him last year. He declined the offer and found a place to sign with the Bucs instead. He never performed up to expectations for the Jets, a team I was stuck with until I got DirecTV five years ago and could watch the Bucs again. If the Bucs use him, he will be okay - but he will never be as accruate as Bryant who is now a 85% accuracy kicker, and still 100% under 40 yards. The Bucs will be happy if Nugent breaks 95% at under 40 yards, mark my words - I watched this guy disappoint NY fans for too many years. Clutch kicking he is not the best... just watch and see.