Block copolymer self-assembly is affected by nanoscale confinement, which has long been known to affect interchain entanglements and dynamics of polymers. While most previous work on confined polymer glasses has focused on the properties of homopolymers, the mechanical response of glassy block copolymer thin films is still relatively unexplored. By uniaxially deforming glassy lamellar diblock copolymer films with different morphologies via molecular dynamic simulations, we demonstrate that the toughness of the films with fingerprint morphologies is higher compared to homopolymers and oriented lamellar films due to the increase in the randomness of domain orientations and entanglements. We show that the thickness impact on the mechanical properties of the block copolymers is not as big as that of the homopolymer systems. In the strain localization analysis of the block copolymer films, there are the plastic rearrangements initially clustered at the boundary between the two phases of the lamellae until close to failure when the plasticity transitions to the center of a domain. In the block copolymer systems, crazes in the thinnest films exhibit distinct behaviors compared to thicker films. Our studies of the film mechanics provide molecular insights into how segmental mobility and entanglements interplay with position and morphology to control the mechanics of thin polymer films.