Don't use Shadow Claw and don't use special moves on Haxorus. Guillotine is banned.
Haxorus has an insane 147 base attack and a god awful around 65ish spatk, so Adamant is definitely better than Hasty. Regarding Adamant vs Jolly, I'd choose Adamant. You gain a lot of damage in exchange for not outspeeding max speed 85+ base speed Pokemon.
In terms of what you wanna use, you absolutely want to use Dragon Claw, it's your STAB move and in normal conditions you'll deal more damage with it. Outrage wasn't buffed to 120 BP so avoid it.
For the next three moves, you probably want something to break past steel types, Superpower definitely deals the most damage but the attack and defense lowering factor may slow down a sweep, still a good option to use. Low Kick is the more spammable move but it deals less damage than Superpower in 99% of matchups. Earthquake has the perfect mix of spammability and damage but it leaves you completely helpless against Skarmory.
As for boosting moves, Dragon Dance is pretty solid but sadly you get outsped by the fairly common Scarf Hydreigon even at +1, if you run adamant you may get outsped by the rare Scarf Porygon-Z, but that's still noteworthy , I personally prefer running Swords Dance Adamant as it allows me to break past most walls with ease.
For your last move either Taunt or the other boosting move, I prefer taunt to disrupt phazing and wisps from cofa but Dragon Dance+Swords Dance is insane if you get to pull it off.
Or you can just say fuck it and run a choice item, run Adamant with Choice Band and Jolly with Choice Scarf, Dragon Claw, Superpower, Earthquake Aqua Tail ez