Abusers can spend a lot of time and energy actually planning something like this -- it's not always spontaneous. Noted, the 'beheading' thing is clearly something we associate with Muslim-related terrorism.
I know of several women who are very, very dead from DV. It may have started with a slapping or a kicking or just being pushed up against a wall. But it's hard to please an abuser; they tend to get more and more demanding. I'll bet this guy feels justified in what he's done, and regretful because of what HE lost (wife, job, freedom). Abusers who kill are seldom remorseful. They typically get 7 years because they go to court and try to prove that 'it was her fault'. Women generally get 20 years (because they ARE remorseful, and take responsibility).
The larger picture here is that terrorism and domestic violence appear to be different aspects of the same type of narcissistic and controlling behavior, based on having power over others. Lord, what a bunch of petulant children these terrorists and abusers are. If they don't get other people to do what they want, they figure it's okay to kill 'em.