Mental stress is a major problem in today's society. It is therefore important to determine the mechanisms underlying stress. In this paper, we aim at studying the cardio-respiratory response to mental stress using a nonparametric multivariate time-frequency approach. In addition, partial spectra are considered to separate RR interval variations (RRV) that can be related to respiration from RRV that are unrelated to respiration. The results confirm vagal withdrawal during mental stress and also reveal that the autonomic response to stress is driven by mechanisms both related and unrelated to respiration that are characterized by different response times.