The marine and ocean water pollution with different-sized plastic waste poses a real threat to the lives of the next generations. Plastic, including microplastics, is found in all types of water bodies and in the organisms that live in them. However, given the chemical diversity of plastic particles, data on their toxicity are currently incomplete. Moreover, it is clear that different organisms, depending on their habitat and feeding habits, are at different risks from plastic particles. Therefore, we performed a series of experiments on feeding the gastropod scraping mollusk Littorina brevicula with two types of polymeric particles—polymethylmethacrylate (PMMA) and polytetrafluoroethylene (PTFE)—using a special feeding design. In the PMMA-exposed group, changes in gastrointestinal biochemical parameters such as increases in malondialdehyde (MDA) and protein carbonyls (PC) were detected, indicating the initiation of oxidative stress. Similarly, a comet assay showed an almost twofold increase in DNA damage in digestive gland cells compared to the control group. In mollusks fed with PTFE-containing food, no similar changes were recorded.