Can you do this in all gens?

Question

I'm in red and at one point when I was in wild grass, by mistake I told my venusaur to use cut and it cut 4 squares of wild grass....

Answer 1

Yep, it is possible to cut grass, though not in all gens...
Gen I - III
> It [Cut] can also be used to cut tall grass

Gen IV-V
> Cut can no longer remove tall grass.

It's a fun thing to do :3

Source: bulbapedia

Answer 2

Generation I-III

A Pokémon using Cut can remove a certain type of tree, which acts as an obstacle between the player and their destination. It can also be used to cut tall grass.

So it's normal for you to be able to cut tall grass randomly.

Cut