When a graduate student be a part of a research grant, does he get paid in addition to a university stipend?
In my experience, “guaranteed funding” means that (depending on field) you will be either working for a PI who has grant money to pay you or working as a TA (with the possible exception of your first year, where their may be general department support while you find an advisor). Because graduate stipends are typically on a pay scale, working on a grant can be expected to bring you up to the guaranteed level, but not put you above it. 

To support the guarantee of funding, the university (or a unit within the university) may have a reserve fund with money that can be used to cover gaps in PI funding (which may come with TA obligations).