In order to enhance the application performance of glycidyl azide polymer (GAP) in solid propellant, an energetic copolyurethane binder, (poly[3,3-bis(2,2,2-trifluoro-ethoxymethyl)oxetane] glycol-block-glycidylazide polymer (PBFMO-b-GAP) was synthesized using poly[3,3-bis(2,2,2-trifluoro-ethoxymethyl)oxetane] glycol (PBFMO), which was prepared from cationic polymerization with GAP as the raw material and toluene diisocyanate (TDI) as the coupling agent via a prepolymer process. The molecular structure of copolyurethanes was confirmed by attenuated total reflectance-Fourier transform-infrared spectroscopy (ATR–FTIR), nuclear magnetic resonance spectrometry (NMR), and gel permeation chromatography (GPC). The impact sensitivity, mechanical performance, and thermal behavior of PBFMO-b-GAP were studied by drop weight test, X-ray photoelectron spectroscopic (XPS), tensile test, scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and thermal gravimetric analysis (TGA), respectively. The results demonstrated that the introduction of fluoropolymers could evidently reduce the sensitivity of GAP-based polyurethane and enhance its mechanical behavior (the tensile strength up to 5.75 MPa with a breaking elongation of 1660%). Besides, PBFMO-b-GAP exhibited excellent resistance to thermal decomposition up to 200 °C and good compatibility with Al and cyclotetramethylene tetranitramine (HMX). The thermal performance of the PBFMO-b-GAP/Al complex was investigated by a cook-off test, and the results indicated that the complex has specific reaction energy. Therefore, PBFMO-b-GAP may serve as a promising energetic binder for future propellant formulations.