The mechanisms of failure of a composite sandwich structure subjected to a projectile impact have been investigated. The results reveal the complex interplay between the various damage dissipation mechanisms. The effects of modifying the matrix of the skins with polysiloxane core–shell rubber (CSR) nanoparticles and silica nanoparticles were investigated. Single cantilever beam specimens were tested to evaluate skin-core debonding. The addition of CSR nanoparticles to the matrix beyond 3 wt% causes a change in failure mechanism from sub-interface foam failure to interfacial failure when 6 and 9 wt% CSR are added. The sandwich structures were impacted with an aluminium projectile at 130 m/s. High speed cameras were used to obtain 3D digital image correlation of the back-face. Sectioning and imaging of the panels revealed damage in the form of front skin perforation and delamination, crushing and fracture of the core and back-face skin-core debonding. The impacted specimens also exhibited a transition in failure mechanism relating to rear face skin-core debonding between 3 and 6 wt%. Panels containing low amounts of CSR resulted in increased core cracking, while beyond the transition point, widespread rear face skin-core debonding was observed. At 3 wt% CSR, optimum back face deflection is achieved, and lower front skin delamination is experienced.