The stress relaxation and creep behavior of blank polyurethane (PU) and PU/clay nanocomposites were investigated. The relaxation time spectrum and retardant time spectrum were derived according to the generalized Maxwell model and Voigt model with a Tikhonov regularization method, respectively. The characteristic relaxation time was identified with the corresponding relaxation process. At a small strain, the relaxation was mainly attributed to uncoiling/disentangling of soft segment chain network in the soft phase, with a single characteristic relaxation time in the range of 5–100 s. The increase in the hard segment content leads to a decrease in the relaxation time, and the addition of clay leads to an increase in the relaxation time. At large strains, the multipeak relaxations occurred, and they were attributed to the breakup of interconnected hard domains and pullout of soft segment chains from hard domains, together with the disentangling of soft segment chain network in the soft phase. The creep results are consistent with those of the stress relaxation. The relaxation and creep behavior were related to microphase separation of PU. This study suggested that the relaxation spectrum can be used to examine the complicated relaxation processes for a multiphase and multicomponent polymer system.