If I use another effect to spend the buff on Sett, Brawler, do I get to use his effect, "Spend my buff: Give me +4 Might this turn"?

No, you do not get to use his effect if another card spends the buff.

According to the official FAQ for Sett, Brawler: "Ruling: No, Sett must spend his own buff to activate his ability. Another card spending a buff (like Call to Glory) will not trigger Sett's ability."

Sett's ability is an activated ability that requires you to pay the cost of spending the buff on him to trigger the effect. If an external effect removes or spends that buff, the cost for Sett's ability has not been paid by the ability itself, and therefore the +4 Might effect will not occur.