Why was Mance Rayder given a chance to "bend a knee"
The opportunity for Mance Rayder to "bend the knee" was offered by Stannis Baratheon. And, when Mance was taken back to Castle Black, he was a prisoner of Stannis, and not the Night's Watch.
At that time, Stannis was trying to get Mance Rayder's army to join forces with him in an attempt to challenge Roose Bolton. Because of this, Stannis was willing to let the wildlings live in exchange for Mance Rayder taking the knee and offering his army.
As far as the Night's Watch goes though, they had planned on killing Mance Rayder from the very beginning, ever since Lord Commander Mormont formed a ranger/scout party to go beyond the Wall. I believe Qhorin talks about sneaking into the wildlings' camp and killing Mance Rayder before they can attack the Wall, which then followed with Jon Snow asking if he could tag along.
I would think it would have been more 'sensible' to just dispose of Mance, as a traitor to Watch, and then treat with Tormund Giantsbane as the 'new leader' of the free-folk.
If Mance had just been "disposed of", then, I really don't think that would have motivated Tormund to bend the knee. From the perspective of the Night's Watch, perhaps the reason for execution would be justified, but, from the side of the Freefolk, I don't they'd care, and would be just as upset.
Also, the King-Beyond-the-Wall is elected, so, there's no indication that Tormund would automatically get the title upon Mance Rayder's execution.