This paper introduces a two-stage stochastic quadratic knapsack problem (TSSQKP) with uncertainty in both profits and weights. To overcome the computational difficulties arising from the combined stochastic, binary, and quadratic structure, we propose a solution framework that integrates an adaptation of the progressive hedging algorithm with clustering-based scenario reduction for computing lower and upper bounds. The enhanced progressive hedging algorithm (EPHA) incorporates a rounding procedure and a dynamic penalty update strategy driven by the detection of oscillation and stagnation patterns. In parallel, we propose a clustering framework based on opportunity-cost distances between scenarios, from which we derive the medoid lower bound (\(\mathrm{LB}_{\mathrm{M}}\)), the cluster lower bound (\(\mathrm{LB}_{\mathrm{C}}\)), and the cluster upper bound (\(\mathrm{UB}_{\mathrm{C}}\)). This decomposition breaks the original problem into smaller subproblems, thereby reducing computational time and memory requirements while approximating the solution of the full-scenario problem. To further improve computational efficiency, EPHA is also used to solve the cluster subproblems heuristically; in this case, the resulting upper bound is referred to as the estimated cluster upper bound (\(\mathrm{EUB}_{\mathrm{C}}\)), and the corresponding gaps are interpreted as estimated optimality gaps. Computational experiments on 800 generated TSSQKP instances show that the proposed framework yields smaller gaps than CPLEX under comparable computational conditions. In the EPHA-based clustering framework, the average estimated gaps associated with \(\mathrm{LB}_{\mathrm{C}}\), \(\mathrm{LB}_{\mathrm{EPHA}}\), and \(\mathrm{LB}_{\mathrm{M}}\) are 1.65%, 1.88%, and 2.41%, respectively, compared with an average optimality gap of 35.86% for CPLEX. The computation of \(\mathrm{LB}_{\mathrm{M}}\) is the fastest, with an average execution time of 420.88 seconds, while EPHA provides a favorable compromise between solution quality and computational effort, reducing the average computational time associated with the cluster bounds by approximately 52.7%, from 5156.79 to 2439.10 seconds, while increasing the average estimated gap by only 0.23 percentage points.