We analyze the quantum version of the Landau-Lifshitz equation for damped spin motion using a properly tailored Gisin approach to the dissipative quantum mechanics. Coherent- and squeezed-spin-state evolution for a single spin S and a ferromagnetically coupled spin chain are discussed in detail. The classical limit of the quantum dissipative dynamics is shown to be equivalent to the conventional description, which uses only the diagonal matrix elements for spin operators. The homogeneous and wave-vector-dependent decay of a squeezing parameter in the neighborhood of the ground state is discussed and shown to exhibit long-wavelength instability.