Dimethyl sulfoxide (DMSO), a polar liquid of low volatility, was used as solvent in the synthesis of branched glycidyl azide polymer (GAP) which is a potential energetic binder for rocket propellants. Branched GAP product was purified by an extraction method using dichloromethane to create an organic phase and a mixture of methanol-brine (50:50 in weight) as the extracting solution. The extraction was carried out in four steps, leaving only less than 1% DMSO in the purified branched GAP. The DMSO concentration remaining in the organic phase was deduced from the H-1 NMR spectra taken after each extraction step. Finally, the physical performance of branched GAP was evaluated through the tensile properties, the glass transition temperature, and the thermal degradation of the energetic polyurethanes obtained after curing branched GAP with different isocyanate compounds. The effect of residual DMSO in branched GAP on the tensile properties of polyurethanes was also investigated.