The interplay between crystallization and phase separation has been intensively studied recently. In this study, we extended the research into a dynamically asymmetric blend composed of amorphous poly(methyl methacrylate) (PMMA) and crystalline poly(ethylene oxide) (PEO). The large dynamic asymmetry induces network stress in concentration growth. We find that crystallization is seriously frustrated when it couples with a simultaneous viscoelastic phase separation. In a single quench experiment, normal spherulites grew in a limited temperature range when crystallization was faster, while crystallization was frustrated at deep quenches when phase separation was faster. In a double quench experiment, crystallization was more difficult to occur after the prior phase separation at a higher temperature. The calorimetric results indicated that both melting temperatures and enthalpies of crystallization decreased in the coupled viscoelastic phase separation. We propose that it is the network stress in the concentration growth that leads to the frustration of crystallization.