We introduce the Dynamic Spectral-Parsing Graph Neural Network (DspGNN), a novel model that innovatively incorporates spectral-designed graph convolution for representation learning and edge regression on Discrete Time Dynamic Graphs (DTDGs).Our first major contribution is the adaptation and optimization of spectral-designed methods to better capture evolving spectral information on DTDGs. Secondly, to solve the computational challenge of performing eigendecomposition on large DTDGs, we propose a novel technique, Active Node Mapping, that proves to be both simple and effective.Our model consistently outperforms baseline methods on three publicly available datasets for edge regression tasks. Finally, we discuss future challenges and prospects in this under-explored field.