The objective of this study was to introduce and demonstrate a computationally efficient, multistep uncertainty quantification approach for high-fidelity, hypersonic reentry flow simulations, which may include large numbers of aleatory and epistemic uncertainties. The multistep uncertainty quantification approach included several key components, including a sensitivity-based dimension reduction process that used a local sensitivity analysis at selected sample locations to approximate global sensitivities. Other components included a method to update existing deterministic samples after dimension reduction and a modified point-collocation nonintrusive polynomial chaos method that incorporates existing local sensitivity information. The multistep uncertainty quantification approach was demonstrated on two model problems. The first was a model for stagnation point convective heat transfer in hypersonic flow. Mixed uncertainty quantification analysis results in reduced dimensions compared well with Monte Carlo simulations. The second problem was a high-fidelity, computational fluid dynamics model for stagnation point radiative heat flux on a Hypersonic Inflatable Aerodynamic Decelerator during a Mars entry. The model consisted of 93 uncertain parameters, coming from both flowfield and radiation modeling. The model was reduced to ten and five uncertain variables, accounting for 95 and 90% of the total output variance, respectively. Pure aleatory, epistemic, and mixed uncertainty quantification analyses were in agreement with previous work, proving the potential and applicability of the multistep uncertainty quantification process for complex hypersonic reentry flow models.