The mutualistic symbiotic radio (SR) with hybrid active-passive communications (HAPC) enables Internet of Things (IoT) devices to share the energy and spectrum resources with the primary transmitter (PT), thus overcoming the spectrum and energy limitations of the IoT devices. However, the minimization problem of PT's transmit power, which can reduce operational costs from the network operator's perspective, has not been addressed. In this paper, we propose to minimize the PT's transmit power in a mutualistic SR network with HAPC. Specifically, we formulate a non-convex problem to jointly optimize several variables, including the PT's transmit power, the operation time of pure energy harvesting (EH), backscatter communications (BC) and active communications (AC) phases, as well as the reflection coefficient and AC's transmit power of each IoT device, and solve it by the following two steps. First, we employ successive convex approximation (SCA) and introduce auxiliary variables to transform the formulated problem into a convex one at a given the PT's transmit power. Second, an iterative algorithm, which combines the bisection and SCA, is proposed to determine the optimal PT's transmit power. The simulation results prove the fast convergence of our proposed algorithm, and show that our proposed scheme achieves a lower PT's transmit power compared to the baseline schemes.