We investigate the microresponse of the quasi-two-dimensional dusty plasma liquid around freezing to the shear force from a laser beam through the center of the liquid cluster. It is found that the cold liquid can be viewed as a patchwork of crystalline ordered domains (CODs) which are solidlike but can be cracked and rearranged by weak thermal agitation and external stress, through COD rotations and drifting. Under weak external stress comparable to thermal agitation, the laser zone is not the preferred region mastering cracking initiation. CODs in the laser zone can either break locally, or sustain and propagate the stress to remote regions for cracking, in the form of intermittent bursts. The COD rotation and drifting induced by the persistent torques and momentum from the stress causes the formation of the center shear band with a higher longitudinal speed. Increasing stress can enhance cracking initiation around the shear zone and then spread to other remote regions. It deteriorates the local structural order and causes strong shear banding dominated by longitudinal cooperative hopping.