A time-dependent angular analysis of $B_s^0topsi(2S)phi$ decays is performed using data recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0invfb collected during Run 1 of the LHC. The CP-violating phase and decay-width difference of the $B_s^0$ system are measured to be $phi_s = 0.23^{+0.29}_{-0.28} pm 0.02$ rad and $DeltaGamma_s = 0.066^{+0.041}_{-0.044} pm 0.007$ ps$^{-1}$, respectively, where the first uncertainty is statistical and the second systematic. This is the first time that $phi_s$ and $DeltaGamma_s$ have been measured in a decay containing the $psi(2S)$ resonance.