In the present study, we consider a two-dimensional nonlinear prey-predator model with harvesting on both the species and specifically with the mortality rate of the predator species. The purpose of this work is to offer mathematical analysis of the model and to discuss some of the vibrant qualitative results that are expected to arise from the inter-play of the biological internal and external forces. Here, all the possible equilibrium points of the model are identified and the criteria for the local as well as global stabilities are investigated. Apart from this, the existence of bio-economic equilibrium with optimal scheme has been critically discussed here. We studied the analytical estimates for the population intensities of fluctuations by Fourier transform methods through stochastic perturbations. We have also highlighted the diffusive stability of the system along with some numerical simulations. Copyright © 2016 Inderscience Enterprises Ltd.