Set priority for an SQL Server role
Unfortunately for you, it does not work that way. Users in multiple roles are subject to the complete set of permissions from all of their roles, and deny permissions always trump grant permissions. You have to keep that in mind as you design your user and role assignments.

In this case, you might find that you don't need the DENY rule at all. A user can't do anything without explicit grant permissions, so if you remove the deny rule from your staff role they likely still won't be able to delete anything: the rule is redundant for them.