The most obvious reason is because Mienshao doesn't get enough usage in NatDex UU. However, there are reasons why Mienshao isn't used in NatDex UU.
On paper, Mienshao seems like it would be good in NatDex UU. Having a great ability in Regenerator, having access to Knock Off, and coverage moves such as Stone Edge, Poison Jab, and Blaze Kick. However, there are things that that make this Martial Arts Pokemon not good as it was in Gen 8 NatDex UU.
1. Pokemon who can tank Mienshao's attacks: Pokemon such as Clefable, Buzzwole, Slowbro, Enamorus, Mega Latias, etc can switch into Close Combat. Even though Mienshao can use Knock Off on them to cripple them, some Pokemon such as Clefable, Buzzwole, Mega Latias, and Slowbro don't mind switching into a Knock Off.
2. Pokemon outclass Mienshao:
Because Pokemon can tank Mienshao's attacks, it would have to be a Pokemon who spams U-turn. However, as an offensive pivot, Cinderace outclasses it despite not having access to Regenerator. As a Fighting-type, Mienshao is outclassed by other Fighting-types such as Buzzwole, Iron Hands, and Galarian Zapdos. Buzzwole and Iron Hands have a secondary type that helps them check opposing Pokemon. Galarian Zapdos, despite being slower than Mienshao, has a secondary type of being a Flying-type to hit Pokemon who resist its Fighting STAB.
TL;DR Mienshao is in NatDex RU since it doesn't get much (if any) usage in NatDex UU since Pokemon such as Clefable, Slowbro, Mega Latios, and Buzzwole can switch into its moves. Mienshao is also outclassed as an offensive pivot and a Fighting-type since the Fighting-types that are used have secondary typing that helps them be offensive or defensive.
Hope this helps.