Triplochiton scleroxylon, commonly known as Ayous, is a tropical non-edible biomass that generates many residues when exploited. These residues have added value when the different lignocellulosic components, cellulose, hemicellulose, and lignin, are separated. This work aims to determine the optimal conditions for microwave-assisted extraction (MAE) of cellulose and hemicellulose biopolymers from Ayous sawdust. The one-factor-at-a-time methodology was used to establish the ranges for the principal factors affecting microwave-assisted extraction, namely microwave power (W), irradiation time (min), and NaOH concentration (%). Subsequently, response surface methodology, specifically central composite design, was employed to determine the optimal extraction conditions for the biopolymer’s cellulose and hemicellulose. The biopolymers obtained under these optimal conditions were then characterized using infrared spectroscopy. The results indicated that, after factor screening, the experimental domains were microwave power 500–600 W, irradiation time 30–40 min, and NaOH concentration 20–30%. Optimal conditions were found to be 466 W of power, 39 min of irradiation, and 33% NaOH concentration, which resulted in extraction yields of 88% for cellulose. Optimum extraction conditions for hemicellulose (75%) are identical to those for cellulose but with a shorter irradiation time of 26 min. Infrared analysis of biopolymers obtained under initial conditions revealed functional groups characteristic of synthetic biopolymers. In conclusion, the study provides a robust methodology for optimizing MAE processes, offering valuable insights for the efficient recovery of high-quality biopolymers from lignocellulosic biomass.