Due to the beam cleanup effect, brightness enhancement (BE) can be achieved in a Raman fiber amplifier (RFA) based on multimode (MM) graded-index (GRIN) fiber. In this Letter, a novel, to the best of our knowledge, diagnostic tool of mode decomposition (MD) based on a stochastic parallel gradient descent algorithm is demonstrated to observe the beam cleanup effect in a GRIN-fiber-based RFA for the first time, to our knowledge. During output power boosting up to 405 W at 1130 nm, the output beam quality factor M2 improves from 3.45 to 2.88, with a BE factor of 10.5. The MD results based on the near-field beam profiles from RFA indicate that the modal weight of the fundamental mode increases from 74.5% to 87%, confirming that the fundamental mode dominates with higher Raman gain. Moreover, the beam quality is found to be limited by the existence of a higher-order (Laguerre-Gaussian) LG10 mode, which is insensitive to the beam cleanup effect. The correlation coefficient reaches over 0.98 for all MD results. Thus, the accuracy of the MD method is high enough to provide further valuable insight into the physics of spatiotemporal beam dynamics in MM GRIN fiber.