Gaining control over precise and predictable structures of colloidal systems and understanding the abundant dynamic behaviors remains a formidable challenge In this study low-frequency mechanical spectroscopy was applied to investigate the dynamics of aqueous solutions of N-isopropylacrylamide-acrylic acid (NIPAM-AA) copolymers with three different AA contents. A mechanical loss valley was found for the solution with low molar fraction of AA (f(AA)), f(AA) = 25 and 50 mol %, and a loss peak was shown for the solution with f(AA) = 75 mol %. The former is suggested to be due to the particle glass phase of repulsive micelles above the low critical solution temperature, whereas the latter is associated with the alpha relaxation behavior of NIPAM-AA/water mixture at high concentrations. The relaxation time of the alpha relaxation seems to follow a simple Arrhenius temperature dependence. The activation energy H is similar to 53 kJ/mol, and the larger H value is suggested to be due to multiple strong hydrogen bonds in the copolymer solution. The present work demonstrates that by controlling the proportion of ingredients in the colloidal systems the systems can exhibit distinct dynamic behaviors, which is helpful in the design and fabrication of colloids.