Understanding and exploiting the competition and allelopathic effects of toxic substances on marine aquatic ecosystems or biodiversity in the soil or among plants is a major challenge in microbial biology and ecology. In this work, we focus on a model of the chemostat of two toxin-producing microbial species competing for a single nutrient. Each species produces toxin which affects the growth of the other species as well as its growth. Removal rates are distinct and include the specific mortality rate and autotoxicity of each species. Our study provides a complete analysis of the model by analyzing the joined effects of competition, allelopathy, and mortality. Using general monotonic growth rates, the mathematical study establishes the conditions of existence and local stability of all equilibria according to the control parameters. The model can present the multiplicity of the coexistence steady states. Numerical simulations show that the three-dimensional system can exhibit bistability where the asymptotic behavior of the system depends on the initial condition.