The sugar shake Varroa mite treatment is a "biological" method based on the natural mite reproductive cycle and bee self-cleaning behavior, based on
Reproduction. Mites reproduce on a 10-day cycle. In 12 weeks the number of mites in a Western honeybee hive can roughly multiply by 12.
You might want to read the full text on Varroa mite athttp://en.wikipedia.org/wiki/Varroa_destructor
In the wikipedia article, go to the heading of Life Cycle and click on the link (A Look under the cap) provided to find more/detailed information about mite reproduction.
What makes the sugar treatment work is
a) the powdered sugar dust triggers the natural bee behavior of cleaning themselves (the bees feel "dirty" due to the sugar dust on their bodies). During the cleaning exercise, mites are "cleaned off" from their bodies together with the sugar dust by the bees and drop down. Sugar treatment in combination with SBB's work best as the mites will usually fall right out of the hive.
b) 10-day treatment cycle. The bees can but clean the mites on their bodies. Mite eggs and larvae inside cells are not affected. For that reason you repeat sugar dusting every ten days, that is to get at those mites having hatched and emerged in the meantime.
Sugar dusting does not kill the mites. What does for them is that they either fall through the SBB and completely out of the hive or if they fall on their backs. If they fall onto their back, they cannot right themselves on their own and die. Obviously, sugar dusting does not produce 100 percent kill rate, it only reduces infestation levels (if done right, to levels non-critical for a colony to survive). The dusting is repeated several times to get some more of those that escape.