You don't negotiate from a position of weakness and that is exactly what Mincey did. The Cowboys have a litany of defensive ends ready to take Mincey's reps in training camp. Did he play well for us last year? Sure, well enough that you want to extend him significantly (i.e. years or money) when you have so much young potential and talent at the position, and having to probably pay Hardy a song next year?
I might extend him an additional year without significant guarantees, but that is as far as I would go for a 31 year old defensive who will be turning 32 by the end of the season. The guy saw the writing on the wall, and I hope his agent didn't back this move. He was still penciled in as a starter for the first 4 games. He should have come out, showed that at a much lighter weight that he could become a more dominant player, and then signed a 2 or 3 year deal with someone for decent money.
You might have to move Mincey over to the strong side given what we're working with here.
Maybe you bump his salary up to 2 million this year as to not leave him embarrassed after that boneheaded move and give him a 1 year extension at 1.5-2 million, with a signing bonus of 1 million.