This is said, not for the beasts, which are not capable of a law, but to restrain the presumption and curiosity of the people, by this argument, that even the beasts that come too near shall be destroyed, and much more man, whose knowledge aggravates his sin and punishment.
Related Commentaries of Exodus 34:3
Exodus 34:3
3 And no man shall come up with thee, neither let any man be seen throughout all the mount; neither let the flocks nor herds feed before that mount.