The behavior of lamellar materials under strain is not yet completely understood, either for large shears where macroscopic defects (onions, focal conic domains) are formed, or even in small-strains experiments where the deformation is ruled by dislocations. We have developed a micro-plasticity experiment, in which we impose a controlled strain to an homeotropic smectic A sample and observe, under microscope, the associated motion of edge dislocations (a dynamical extension of the well-known experiment [1] at rest described in R. B. Meyer et al., Phys. Rev. Lett. 41, 1393 (1978)). We note that edge dislocations are strongly pinned by screw dislocations. We explain how this pinning is at the origin of a yield strain. We furthermore study the dynamics of climbing edge dislocations and evidence a morphological transition from a jerky motion to a viscous regime. We clarify the role of the pinning in this transition.