We report our studies of coherent acoustic phonons (CAPs), generated and time-resolved–-detected in semimagnetic Cd_1-xMn_xTe single crystals by means of femtosecond pump-probe spectroscopy. On crystals with concentrations x = 0.01, 0.05 and 0.09, we implemented one-colour spectroscopy, where photon energies of both the pump and probe beams were the same and either just above or below the energy gap of the crystals. For Cd_0.91Mn_0.09Te we have also performed two-colour spectroscopy, in which the pump/probe photon energies were far above/below the CdMnTe bandgap, respectively. The dependences of both the frequency and dephasing time of CAP oscillations on the probe wavelength were consistent with the propagating-strain–-pulse model. In one-colour experiments, we observed a nonlinear dispersion relationship between the measured CAP frequency and the probe wave vector, which was due to a strong wavelength dependence of the probe beam on the refractive index n near the CdMnTe bandgap. The functional dependence of n, extracted from our experiments, could be fitted very well by the Schubert model. Our two-colour pump-probe measurements showed that the penetration depth of probe light, rather than the intrinsic decay time of CAPs, was the dominant source of the oscillation dephasing time. The lifetime of CAPs in our crystals was found to be at least on the order of nanoseconds. We experimentally validated that the electronic stress was the dominant generation mechanism of CAPs in CdMnTe crystals and observed that the value of the sound velocity increased with the increase of Mn-ion concentration in our samples.