Higher-order interactions have significant implications for the dynamics of competing epidemic spreads. In this paper, a competing spread model for two simplicial irreversible epidemics (i.e., susceptible-infected-removed epidemics) on higher-order networks is proposed. The simplicial complexes are based on synthetic (including homogeneous and heterogeneous) and real-world networks. The spread process of two epidemics is theoretically analyzed by extending the microscopic Markov chain approach. When the two epidemics have the same 2-simplex infection rate and the 1-simplex infection rate of epidemic A ( λ) is fixed at zero, an increase in the 1-simplex infection rate of epidemic B ( λ) causes a transition from continuous growth to sharp growth in the spread of epidemic B with λ. When λ > 0, the growth of epidemic B is always continuous. With the increase of λ, the outbreak threshold of epidemic B is delayed. When the difference in 1-simplex infection rates between the two epidemics reaches approximately three times, the stronger side obviously dominates. Otherwise, the coexistence of the two epidemics is always observed. When the 1-simplex infection rates are symmetrical, the increase in competition will accelerate the spread process and expand the spread area of both epidemics; when the 1-simplex infection rates are asymmetrical, the spread area of one epidemic increases with an increase in the 1-simplex infection rate from this epidemic while the other decreases. Finally, the influence of 2-simplex infection rates on the competing spread is discussed. An increase in 2-simplex infection rates leads to sharp growth in one of the epidemics.