Differential Evolution (DE) has established itself as a very useful tool in the domain of optimization technique in recent times. It has found its paramount importance in various signal processing applications. Amongst them, design of Finite duration Impulse Response (FIR) filter using DE algorithm has drawn special interest in recent times. In this paper, we have analyzed the impact of various mutation strategies of DE algorithm for the design of linear-phase low pass FIR filter. The performance of this evolutionary optimization technique has been evaluated in terms of its convergence behaviour for different mutation schemes. Additionally, the behaviour of the designed filter under different mutation strategies has been analyzed by studying its magnitude and impulse response. Finally, the most suitable mutation scheme has been suggested for this specific design problem.