The key here is the larger male getting a grip with his jaws on the back of the female’s neck. He doesn’t let go. In this encounter, a series of skirmishes interspersed bouts of wrestling with periods of rest. All the while the male maintained a firm grip.
After one tussle, the male lost his footing and ended up hanging off the back of the female, his jaws still clenched on her neck. The female hung on with a couple of claws, as they swung side to side. Then she lost her grip.
The pair plunged onto a ti plant where the male immediately puffed out his dewlap. The female took the opportunity to scamper off. He pursued for a while but lost track of her and gave up. The female meanwhile looked somewhat the worse for wear, a clump of darkened skin bunched up from her neck.
Clearly anoles are one species where relationships can literally be a pain in the neck!
For more information about green anoles, go to en.wikipedia.org/wiki/Carolina_anole.