Low-energy spin excitations were investigated in the static stripe phase of La2-xSrxCuO4 using elastic and inelastic neutron scattering on single crystals. For x=1/8 in which long-range static stripe order exists, an energy gap of E(g)=4 meV exists in the excitation spectrum in addition to strong quasielastic, incommensurate spin fluctuations associated with the static stripes. When x increases, the spectral weight of the spin fluctuations shifts from the quasielastic continuum to the excitation spectrum above E(g). The dynamic correlation length as a function of energy and the temperature evolution of the energy spectrum suggest a phase separation of two distinct magnetic phases in real space.