Insults of low blood flow to the gut can ultimately lead to digestion issues, but not commonly from medication use like you are asking about. Certain medications affect the digestive system by limiting blood flow as a side effect, although not typical blood thinners like heparin or warfarin or riveroxiban. NSAIDs such as aspirin and ibuprofen (which do have mild "blood thinning" effect-although unrelated) do constrict gastric blood flow and lead to increased risk of gastric ulcers and are recommended to be taken with food. If blood pressure does get too low (usually in the case of shock), certain areas of the large intestine can die and bleed from lack of blood flow causing digestive issues. In addition, sometimes people with really bad vascular disease like atherosclerosis or high cholesterol can get stomach pain after they eat because the digestive system is demanding more blood flow than their arteries can give them. As other commenters have already mentioned, "blood thinners" are anticoagulants, meaning they make it harder for your blood to clot. Beta blockers work by slowing down the heart and allowing veins to dilate. Neither of these mechanisms directly affect blood flow to your digestive system.