The action of NaCl vs KCl on the static and kinetic behavior of a fully charged and unfolded polyglutamic acid (PGA) chain is investigated by extensive explicit-water computer simulations. Ion-specific shrinking of the PGA coil size with increasing salt concentration is observed and is consistent with intrinsic viscosity measurements. The PGA relaxation kinetics is found to be nearly exponential in KCl on a Rouse/Zimm time scale (similar or equal to 1 ns), whereas NaCl induces a 10- to 100-times slower, highly nonexponential relaxation. The slow decay can be traced back to Na+ ions bridging anionic groups with scale-free power-law residence time distributions. This "transient cross-linking" may explain cation-specific slowing down of (bio)polymer kinetics observed in a variety of experiments. A systematic test using different force-field combinations in the simulations corroborates the qualitative trends, while quantitatively, the kinetic rates in the NaCl simulations significantly depend on the particular choice of water and ion parameters.