In this paper, we present an isogeometric analysis framework for design space exploration. While the methodology is presented in the setting of structural mechanics, it is applicable to any system of parametric partial differential equations. The design space exploration framework elucidates design parameter sensitivities used to inform initial and early-stage design. Moreover, this framework enables the visualization of a full system response, including the displacement and stress fields throughout the domain, by providing an approximation to the system solution vector. This is accomplished through a collocation-like approach where various geometries throughout the design space under consideration are sampled. The sampling scheme follows a quadrature rule while the physical solutions to these sampled geometries are obtained through an isogeometric method. A surrogate model to the design space solution manifold is constructed through either an interpolating polynomial or pseudospectral expansion. Examples of this framework are presented with applications to the Scordelis–Lo roof, a Flat L-Bracket, and an NREL 5 MW wind turbine blade.