Advances in robot teleoperation have enabled groundbreaking innovations in many fields, such as space exploration, healthcare, and disaster relief. The human operator's performance plays a key role in the success of any teleoperation task, with prior evidence suggesting that operator stress and workload can impact task performance. As robot teleoperation is currently deployed in safety-critical domains, it is essential to analyze how different stress and workload levels impact the operator. We are unaware of any prior work investigating how both stress and workload impact teleoperation performance. We conducted a novel study ($n=24$) to jointly manipulate users' stress and workload and analyze the user's performance through objective and subjective measures. Our results indicate that, as stress increased, over 70% of our participants performed better up to a moderate level of stress; yet, the majority of participants performed worse as the workload increased. Importantly, our experimental design elucidated that stress and workload have related yet distinct impacts on task performance, with workload mediating the effects of distress on performance ($p< .05$).