It's been a long time since I read this. It's a satirical take on the the military scifi like Starship Troopers. As I remember, a farmhand gets talked into joining up for the Space Army (or whatever it's called) and embarks on a series of wacky misadventures. At one point he loses his arm very heroically. Unfortunately the hospital is all out of right arms and he ends up with a left arm for a right arm.
Pretty much every other depiction of Bill I've ever seen is a satirical recruitment poster sort of thing. A happy soldier smiling and saluting with an upside down hand. The artist here went in an odd direction. Turning Bill into a grotesque. I don't feel it captures the spirit of the book at all. I've always felt the the artist hadn't actually read it. He or she was probably given a broad strokes description and a brief description of the character. "It's a military scifi thing. Oh, and the main character has two left arms."
I've never actually liked this cover that much. Mostly it's the arm thing. Also the face.