The main reason that the deep breathing associated with snoring makes you tired is because of the Bohr effect.
Snoring is the sound made by a person breathing more air than is required for the low metabolic level of sleep, and so it causes a slight drop in carbon dioxide. This slight drop makes haemoglobin stickier, and less likely to release sufficient oxygen to the working muscles.
This is why the chronic snorer often has sore chest, shoulders, neck and back muscles. The muscles are being asked to work for long periods with less oxygen, and so they make more lactic acid. An increase in lactic acid production causes fatigue.