An explicit evaluation of the deuteron spin asymmetry and the associated Gerasimov–Drell–Hearn (GDH) integral for coherent and incoherent π-photoproduction channels with inclusion of rescattering effects is presented. The helicity-dependent total inclusive photoabsorption cross section on the deuteron and the helicity-dependent semi-exclusive channels γd→π^±NN and γd→π⁰X (X=pn or d) are explicitly evaluated up to 1.5 GeV. Our model calculations indicate that convergence of the GDH integral is reached for π⁰-production, while it is not completely reached for π^±-production. For the sum of γd→πNN and γd→π⁰ d contributions to the finite GDH integral by explicit integration up to 1.5 GeV, a value of 249.73 μb is obtained. The extracted results are compared with available experimental data from MAMI and ELSA. We find that our predictions fairly well reproduce the data in the π^± NN case, while fail to predict the measured shape of the π⁰X channel.