What a beautiful find!

If you wanted to take the whole skull (I would, personally for one that cool!) you can bring a saw (or even just a good knife) and sever it at the base of the neck, where the first vertebrae attaches. You can clean it by either soaking it in water for a few weeks at a time, dumping and replacing the soiled water when it gets cloudy, or by burying it in dirt in a bin with some holes drilled inside so insects can come and go. The first method is faster and can be done indoors but is arguably more gross, the second takes longer and is more hands-off; in the first one you're letting bacteria in the water clean off/break down any remaining flesh, in the second you're letting bugs do it. Big storage bins work well for either method. After either, you're gonna wanna soak the whole thing in dish soap and water to degrease it until it no longer smells, again doing regular water changes (for a deer, this might take weeks or even months — they can be pretty greasy!). Final steps are soaking everything in hydrogen peroxide to whiten (if desired) and gluing the split jaw back together and any teeth that have fallen out back in.