Mental stress is a growing problem in our society. In order to deal with this, it is important to understand the underlying stress mechanisms. In this study, we aim to determine how the cardiorespiratory interactions are affected by mental arithmetic stress and attention. We conduct cross time-frequency (TF) analyses to assess the cardiorespiratory coupling. In addition, we introduce partial TF spectra to separate variations in the RR interval series that are linearly related to respiration from RR interval variations (RRV) that are not related to respiration. The performance of partial spectra is evaluated in two simulation studies. Time-varying parameters, such as instantaneous powers and frequencies, are derived from the computed spectra. Statistical analysis is carried out continuously in time to evaluate the dynamic response to mental stress and attention. The results show an increased heart and respiratory rate during stress and attention, compared to a resting condition. Also a fast reduction in vagal activity is noted. The partial TF analysis reveals a faster reduction of RRV power related to (3 s) than unrelated to (30 s) respiration, demonstrating that the autonomic response to mental stress is driven by mechanisms characterized by different temporal scales.