In many applications, such as aerospace and additive manufacturing, polymeric materials with nanoscale structures can be subjected to extensive plastic deformations and present nonlinear dynamic responses under high-strain-rate adiabatic conditions due to nanostructure changes and temperature-dependent material properties. Their rate-dependent characteristics are determined not just by volumetric plastic deformation but also by the resultant thermal effects in the excessively deformed region. Hence, the dynamic nonlinearity of model polymeric systems, microparticles of multiphase block copolymers, is systemically investigated using the Laser-Induced Projectile Impact Tests with perpendicular (α-LIPIT) and non-perpendicular (θ-LIPIT) incidence angles in this study. The polystyrene-block-polydimethylsiloxane (PS-b-PDMS) copolymers are the model materials consisting of mechanically distinctive nanoscale domains of PS (glassy-phase) and PDMS (rubbery-phase), and the visco-plasticity during impact is quantified through mechanical and rheological analysis. The α-LIPIT produces precisely controlled high-strain-rate collision conditions, and the kinetic parameters are used to analyze the mechanical behaviors of the block copolymer microparticles in the forms of the coefficient of restitution and adhesion windows. Furthermore, the newly introduced θ-LIPIT results with a non-perpendicular incidence angle demonstrate the effect of tribological nonlinearity on adhesion mechanisms through the rheological analysis representing the collision-induced thermal condition changes such as thermal softening. The glassy domain controls the rheological transition, while the rubber domain enhances interfacial conditions and is favorable for adhesion. The microparticles’ post-impact shape changes are used to optimize material parameters for a computational model. The nanostructure changes are directly analyzed after cross-sectional milling with a focused ion beam to understand the stress flow and the effective thermal softening region during impact. This study offers a comprehensive understanding of nanostructured block copolymers’ plastic and adhesion mechanisms for use in high-strain-rate additive manufacturing, such as cold spray. The verified correlations between adhesion and compositional and tribological properties are expected to be used to investigate the applicability of feedstock materials and optimize the material parameters for cold spray.