How would I go about doing that?

Most modern permission plugins allow you to revoke default permission, this including VeinMiner's default permissions. See the description for a list of permissions that grant access to vein mining. veinminer.veinmine.<tool>. Consult your permission plugin's guide on node negation.

I am able to revoke permissions. However, if I revoke permissions from the default rank and have a donor rank integrate the default rank, even if the donor rank has the permissions to use it, they cannot.