Before anything else, we have a Homebrew forum so this should probably be moved there. You can just ask a mod to do that for you.

Level 3:
- Losing proficiencies is basically not a done thing in 5e. Virtually everything is geared towards forward progression, this would mean you have two levels where you are more capable then suddenly lose that capability
- Fighting style is fine. Barbarians don't get one so its useful, but it isn't really impressive
- Favored enemy by another name, and Favored Enemy has a reputation as a mediocre-to-poor feature. You at least expand on this at later levels so that's something, but it's still a hit-or-miss sort of thing that doesn't help you slay these creatures until level 14.

At this stage, there is basically no real reason to want to pick this subclass at level 3. There isn't anything here with bite, not even compared to the maligned Berserker or Battlerager (which is coincidentally also Dwarf-only).

Stout-Hearted is a good feature, giving you much needed assistance avoiding things that commonly shut down barbarian and importantly isn't reliant on Rage.

The first part of Grudgelord is a solid soft-control, but the second part is also a self-nerf. You're mechanically forcing the player to make what sounds like an RP decision, i'd recommend dropping the save for the Barbarian and just having your Slayer Prey save or not being able to move more than 30 feet away, like a poor-mans Conquest Paladin.

Mighty Blow could just be applied to everything while raging and not purely against your Prey, else this recreates the Foe Slayer problem (though thankfully to a lesser degree).

Overall, the concept sounds solid and there is some potential here but it needs a bit of polish to fit in against other options (both other Barb subclasses and other things like MCing into Ranger).