We present a theory for the dissipation of electronic spins trapped in quantum dots due to their coupling to the host lattice acoustic phonon modes. Based on the theory of dissipative two level systems for the spin dynamics, we derive a relation between the spin dissipative bath, the electron confinement, and the electron-phonon interaction. We find that there is a sharp bath resonance at an energy which is typically much smaller than the electronic lateral confinement energy. We show that this resonance can be easily tuned to the Zeeman frequency of the spins, and that it sets the boundary between two different dissipative regimes.7019