Until recently, it was widely published that V. destructor fed on the hemolymph ("bee blood") of capped bee larvae as they metamorphosed into adults. Under the wax capping of the pupal stage, the Varroa females feed on the bee larvae and lay their eggs which develop, mature and mate before the newly formed adult bees emerge.
However, it is not the "blood" of the larvae on which the Varroa feed, but on the fat bodies of the larvae. The Varroa insert their mouthparts into the larvae and secrete digestive enzymes into the fat bodies which digest that organ inside the larval bodies. Then, the Varroa re-ingest the enzymes with the extra-orally digested fat body tissues of the larva.
An exceptional explanation of this is given by Dr. Samuel Ramsey: Varroa feed on Fat Body - lecture at the INIB honey show 2019