Mosaic blur/pixelate a material without using UVs

Maybe with a bit of custom HLSL.
Short of that, if the UV has been assinged I don’t think the engine has anything built in that lets you re-sample or change it.

Still, its not a “normal” operation. After you assing a UV to a texture you can’t really change that assignment since the sample is created and loaded into Vram for use.

You probably need to convert from the Vertex Paint to the UV related value to use or better yet, apply the vertex color stuff after the effect you want is already in place.

So…
The only thing that lets you re-sample already sampled stuff is acrually a post process.
Potentially you can toss the mesh you want this effect of in a stencil, then have the post process active just on that stencil.

But. Its about 300 times more expensive than it would be to output the right UV in the first place…