Filters play a crucial role in signal processing, and finite impulse response filters are particularly useful for their stability, linear phase characteristics, and ease of hardware implementation. This research proposes a hybrid and dynamic mutation strategy within the Differential Evolution framework to determine the optimal filter coefficients to minimize ripples in both the pass-band and stop-band. In the standard form of Differential Evolution, the loss of diversity over time leads to a diminished strength of the differential vector and restricts the level of exploration. Hence a dynamic mutation rate with increasing tendency has been proposed to amplify the differential vector effect and is very useful, particularly at the later stage of evolution. The high level of divergent exploration by randomly sampled solutions in differential vector formation slows down the convergence hence the proposed work under probabilistic environment integrated the exploration of surrounding space near the available best solution to make convergence faster and optimal. The linear programming-based optimization model has been formulated to design the desired filter and the performances of the proposed solution were compared against dynamic weighted Particle Swarm Optimization and self-adaptive Evolutionary Programming mutated with Gaussian and Cauchy distribution. The results indicate that the proposed solution demonstrates excellent superior performances under various design criteria and delivered frequency response with ripples of 0.0254 dB in the pass-band and −50.1497 dB in the stop-band along with faster convergence and high success rates.