Recent experimental data demonstrate emerging magnetic order in platinum atomically thin nanowires. Furthermore, an unusual form of magnetic anisotropy-colossal magnetic anisotropy (CMA)-was earlier predicted to exist in atomically thin platinum nanowires. Using spin dynamics simulations based on first-principles calculations, we here explore the spin dynamics of atomically thin platinum wires to reveal the spin relaxation signature of colossal magnetic anisotropy, comparing it with other types of anisotropy such as uniaxial magnetic anisotropy (UMA). We find that the CMA alters the spin relaxation process distinctly and, most importantly, causes a large speed-up of the magnetic relaxation compared to uniaxial magnetic anisotropy. The magnetic behavior of the nanowire exhibiting CMA should be possible to identify experimentally at the nanosecond time scale for temperatures below 5 K. This time-scale is accessible in e.g., soft x-ray free electron laser experiments.