Start or begin, as in We teed off the fundraising drive with a banquet. This usage is a metaphor taken from golf, where
tee off means “start play by driving a golf ball from the tee.” [Second half of 1900s]
Make angry or irritated, as in That rude comment teed him off, or I was teed off because it rained all weekend. [Slang; mid-1900s] Also see tick off.