Bivalves, such as freshwater clams (Corbicula fluminea) and hard clams (Meretrix lusoria), are the most extensive and widely grown shellfish in land-based ponds in Taiwan. However, few studies have examined the contamination of bivalves by quinolone and organophosphorus insecticides. Thus, we adapted an established procedure to analyze 8 quinolones and 12 organophosphorus insecticides using liquid and gas chromatography–tandem mass spectrometry. Surveys in Taiwan have not noted high residual levels of these chemicals in bivalve tissues. A total of 58 samples of freshwater or hard clams were obtained from Taiwanese aquafarms. We identified 0.03 mg/kg of enrofloxacin in one freshwater clam, 0.024 mg/kg of flumequine in one freshwater clam, 0.02 mg/kg of flumequine in one hard clam, 0.05 mg/kg of chlorpyrifos in one freshwater clam, 0.03 mg/kg of chlorpyrifos in one hard clam, and 0.02 mg/kg of trichlorfon in one hard clam. The results indicated that 5.17% of the samples had quinolone insecticide residues and 5.17% had organophosphorus residues. However, the estimated daily intake (EDI)/acceptable daily intake quotient (ADI) indicated no significant risk and no immediate health risk from the consumption of bivalves. These results provide a reference for the food-safety screening of veterinary drugs and pesticides in aquatic animals. Aquatic products should be frequently screened for residues of prohibited chemicals to safeguard human health.