There is a one-time Razor Claw that an NPC in Tapu Village will give you if you have at least 50 TMs.
If you've already used this Razor Claw to evolve a Pokémon, and are now looking for another, then the only other way to get them is through wild Jangmo-o, Hakamo-o, and Kommo-o, who each have a small chance to be holding one. The quickest way to get a Razor Claw this way would be to chain Jangmo-o, since outside of chaining, they only have a 5% encounter rate, and you're likely to need least a handful of them before you find one with a Razor Claw.
The only damaging moves any of them will know are Headbutt and Dragon Claw, so the ideal Pokémon for chaining them is Mimikyu, who also conveniently learns Thief via TM (which can be found in Verdant Cavern). If you decide not to go with Mimikyu, keep in mind that they also know Screech, so the damage could get out of hand if you don't want to switch Pokémon every few turns. For Mimikyu, I would recommend a move set of Thief, Play Rough, and possibly Swords Dance, so that you can ideally start OHKOing Hakamo-o and Kommo-o with Thief as they come in (although I haven't run the numbers and it is a resisted hit, so that might not be possible). Just keep doing this until it says you stole a Razor Claw.
Additional tips in case you're not already aware:
- Jangmo-o can only be found in the tall grass of Vast Poni Canyon. They range from levels 41-44, so make sure your chaining Pokémon is a high enough level.
- Thief can't steal an item if Mimikyu (or whichever Pokémon you decide to use) is already holding an item, so make sure it isn't holding anything.
- Hakamo-o and Kommo-o will not call any new Pokémon if you KO Jangmo-o, so keep the original Jangmo-o alive until you're ready to end the chain.