Popularized by the movie, "The Heathers", this phrase is said in response to a request one deems impossible or absurd (much like being gently fucked with a chainsaw). It's basically a way of showing someone how ridiculous what they've just asked sounds.
Ex.
Veronica: “Why can’t we talk to other kinds of people?”
Heather Chandler: “Fuck me gently with a chainsaw. Do I look like Mother Theresa?”
Dylan: "Hey Nick can I borrow your car once its out of the shop?"
"Fuck me gently with a chainsaw. You crashed it just last week!"
" man you didnt do to well that time"
"Well fuck me sideways with a lunchbox, i made it to the last level man."
"Finally, I would like to comment on an unlikely topic, my pass coverage ratings. I see that I am a better at man-to-man coverage (31) than zone (21). Fuck me sideways with a lunchbox. Where did these scores even come from?" -- Ethan Albright to John Madden regarding him beong the lowest rated player in madden.