Well, I'm not sure if there is verb that describes this movement, but I did dig up something, that might be useful to you:
A common maneuver in a Sword Fight: one character will dodge a sword swipe by bending over backward as the opponent's blade whips horizontally over their body.
I even found the exact image you attached in the question, where I found this term. I'm not sure whether this is an officially valid term, but it seems to fit your description.
This must've been derived from Limbo, a traditional popular dance contest that was known to be originated on the island of Trinidad.
In this dance, a horizontal bar, known as the limbo bar, is placed atop two vertical bars. All contestants must attempt to go under the bar with their backs facing toward the floor. Whoever knocks the bar off or falls is eliminated from the contest. When passing under the bar, players must bend backwards. No part of their bodies is allowed to touch the bar and no part other than their feet may touch the ground. After everyone has completed their turns, the bar is lowered slightly and the contest continues. The contest ends when only one person can successfully "limbo" under the bar without penalty.
Besides this, you could just say:
He dodged the sword swing, by bending/ leaning backwards.