No,

Mimics can only strictly turn into objects, that means things like, doors, door frames, key holes, keys, key rings, door knobs, knockers, peep holes- and those are just the door-and-other-doory-objects Mimics.

But...

Since a dead creature is considered an object, they can turn into a dead creature, if you want. It should be noted that they don't get the creature's stats and attacks.

Creatures that shapeshift

There are many creatures that can assume the form of humanoids and beasts without casting spells: Metallic Dragons and Deva, come to mind. I won't list them here but you can look through the Monster Manual to find the ones with the "Shape Change" trait.

A creature that can cast Shapechange is also a good candidate for what you want, it is, however, a 9th-level spell.

However, it appears what you want to be able to do is to make the mimicking creature appear stronger than it actually is. Most creatures with Shape Change can only look weaker, one exception could be the Doppelganger- taking the form of, say, an Assassin.

For Beholders, specifically...

There is a fungus called Gas Spores found in page 137 of the Monster Manual. They can serve the purpose of mimicking Beholders, as they are described as:

A gas spore is a spherical, balloon-like fungus that resembles a beholder from a distance, though its true nature becomes increasingly obvious as one approaches it.

Have fun freaking out your party!

Yes

The ability is not the Polymorph spell

The weretiger cannot possibly be casting polymorph, because polymorph requires that the target change into a beast. However, the hybrid form is distinctly a humanoid form. We can deduce this because the ability says:

Its Statistics, other than its size, are the same in each form.

Monster statistics include type. Which means that even in tiger form, the weretiger is a Humanoid (Human, shapechanger).

Polymorph says that:

The target's game Statistics, including mental Ability Scores, are replaced by the Statistics of the chosen beast.

If the weretiger were casting Polymorph, its type would change. But it doesn't, so the creature isn't casting Polymorph. Therefore the rules for the Polymorph spell do not apply.

They can use weapons, which is probably good enough for somatic components.

The actions of the weretiger allow for the hybrid form to use weapons, with no penalty compared to their normal humanoid form. If their hybrid hands can wield weapons effectively, then there is no reason that they can't manipulate material and somatic spell components with similar ease.

Hybrid forms can still speak

The stat block for the weretiger allows the creature to speak in all forms except tiger form. Thus, the hybrid form can provide verbal spell components.

So, we have established that the limitations of the polymorph spell do not apply, the hybrid form can use weapons and so should have the dexterity for somatic and material spell components, and they can still speak to provide verbal components. Thus, in hybrid form, a weretiger can cast spells.

All other werecreature hybrid forms follow similar structure as the weretiger to my knowledge, and so should work identically.