The switching of domains in ferroelectric and multiferroic materials plays a central role in their application to next-generation computer systems, sensing applications, and memory storage. A detailed understanding of the response to electric fields and the switching behavior in the presence of complex domain structures and extrinsic effects (e.g., defects and dislocations) is crucial for the design of improved ferroelectrics. In this work, in situ transmission electron microscopy is coupled with atomistic molecular dynamics simulations to explore the response of 71° ferroelastic domain walls in BiFeO3 with various orientations under applied electric-field excitation. We observe that 71° domain walls can have intrinsically asymmetric responses to opposing biases. In particular, when the electric field has a component normal to the domain wall, forward and backward domain-wall velocities can be dramatically different for equal and opposite fields. Additionally, the presence of defects and dislocations can strongly affect the local switching behaviors through pinning or nucleation of the domain walls. These results offer insight for controlled ferroelastic domain manipulation via electric-field engineering.