Magnetic relaxations arising from spin-phonon interactions for a magnetically diluted double-decker terbium phthalocyanine single molecule magnet, dil1, in the nonthermally activated temperature range have been investigated. While the relaxation time, tau, is independent of the external static magnetic field, H-dc, in the high temperature range, where linear relationships between -ln tau and T-1 are observed in the Arrhenius plot, magnetic field dependences for tau are observed in the lower temperature range. The tau(-1) vs H-dc plot at 12 K fits the quadric curve when H-dc < 12 kOe, while linear relationships are observed in the tau(-1) vs T plots in the temperature range of 12-20 K. These results indicate that the direct process is the dominant magnetic relaxation pathway in the nonthermally activated temperature range, while the contribution from the Raman process, if any, is not observable. We emphasize in this paper that the contribution from the thermal relaxation processes and the quantum tunneling of magnetizations (QTMs) to the experimentally observed magnetic relaxations must be evaluated carefully in order to avoid confusion between the thermal and quantum-mechanical relaxation pathways.