Copper compounds are attracting considerable attention in different fields of condensed matter physics due to a number of their unique properties, including superconductivity, complex magnetic phase diagram etc. Copper metaborate CuB2O4 is an outstanding material in the cuprates family owing to its very large complex crystallographic unit cell containing 12 Cu ions occupying two distinct positions, which yields nontrivial magnetic structure. It was shown recently that the response of copper ions at different crystallographic positions can be unambiguously distinguished in the optical spectral range, providing rare opportunity for laser-induced selective excitation of dynamics of different magnetic ions in a solid medium. Here we report on experimental studies of laser-induced spin and lattice dynamics in this material. This research is partly supported by the Program P220 (14.B25.0031.25) and JSPS (13005).