Kinetics of the phase separation in binary off-critical mixtures of polybutadiene (PB) and polyisoprene (PI) was investigated as a function of quench depth and composition by using time-resolved fight scattering. The kinetics for the off-critical mixtures is much slower than that for the critical mixture. The scattering maximum for the off-critical mixtures is very broad relative to that for the critical mixture. For the off-critical mixtures, the domain growth follows the same power law (q(m),similar to t(-alpha), I-m similar to t(beta): alpha=0.25-0.33, beta=0.75-1) in the long time Limit covered in our experiments, independent of quench depth and composition. However, the domain growth became very slow before the long time Limit under a certain condition (intermittency of the domain growth). In the regime where the intermittency was observed, the scaling exponents alpha and beta depend on quench depth. The shallower the quench, the smaller the values of alpha and beta- and the longer the intermittent regime. These behaviors are largely different from those for the critical mixture for which the scaling exponents shaw almost the same value in the late stage for different quenches and the Langer-Bar-on-Miller or Chou-Goldburg scaling postulate is fulfilled. Scaled structure factor in the late stage of phase separation process was found to depend on quench depth, becoming broader as quench is shallower.