Mode of action is all important here. As Will says, the physiological basis may not be known in some cases (e.g. for benzoate and benzyl acaricides), but for others where it is, there are three basic classes of inhibitors, targeting: (1) growth and development, (2) respiration and metabolism and (3) neuromuscular systems and  neurotransmitters. Acaricides that work on mites and not on insects are most likely to do so because of differences between mites and insects in the underlying biochemical detail of the system that is targeted by the acaricide. For example, an acaricide that disrupts a stage in the synthesis of lipids used for the production of eggs might result in fewer/smaller larvae and/or high egg mortality. An extra enzyme or a different co-factor in the lipid pathway in insects means that the acaricide would not work (or not work as well), if that part of the pathway were targeted.     

That really depends on the acaricides.  Some of them are actually general pesticides and will kill insects, mites, and vertebrates at the right concentration.  Some are delivered in such a way as to not be taken up by the insect pests.  Some such as the soaps are more effective against smaller organisms and the mites are smaller than say caterpillars.  Finally to my knowledge some acaricides such as sulfur have poorly known modes of action so why they target mites and not insects is not fully known.

Mode of action is all important here. As Will says, the physiological basis may not be known in some cases (e.g. for benzoate and benzyl acaricides), but for others where it is, there are three basic classes of inhibitors, targeting: (1) growth and development, (2) respiration and metabolism and (3) neuromuscular systems and  neurotransmitters. Acaricides that work on mites and not on insects are most likely to do so because of differences between mites and insects in the underlying biochemical detail of the system that is targeted by the acaricide. For example, an acaricide that disrupts a stage in the synthesis of lipids used for the production of eggs might result in fewer/smaller larvae and/or high egg mortality. An extra enzyme or a different co-factor in the lipid pathway in insects means that the acaricide would not work (or not work as well), if that part of the pathway were targeted.     

It is not general truth, many insecticide may be effective against acarines and acaricides may also act on insects; all depends on biochemistry and physiology of the insect/acarine.