This study investigates the relationship between respiration and autonomic nervous system (ANS) activity and proposes a parallel detection method that can simultaneously extract the heart rate (HR) and respiration rate (RR) from different pulse waves measured using a novel biodegradable piezoelectric sensor. The synchronous changes in heart rate variability and respiration reveal the interaction between respiration and the cardiovascular system and their interconnection with ANS activity. Following this principle, respiration was extracted from the HR calculated beat-by-beat from pulse waves. Pulse waves were measured using multiple biodegradable piezoelectric sensors each attached to the human body surface. The Valsalva maneuver experiment was conducted on seven healthy young adults, and the extracted respiratory wave was compared with a reference respiratory wave measured simultaneously. The experimental results are consistent with the observations from reference waves, where R2 = 0.9506, p < 0.001 for the extracted RR and the reference RR, thus demonstrating the detection capability under different respiratory statuses.