Mutualistic SR is a communication paradigm that offers high spectrum efficiency and low power consumption, where the SU transmits information by modulating and backscattering the PT's signal, enabling shared use of spectrum and power with PT. In return, the PT's performance can be enhanced by SU's backscattered signal, forming a mutualistic relationship. However, the low modulation rate causes extremely inferior transmission rates for SUs. To improve the SU transmission rate, this paper proposes a new mutualistic SR with HAPC to explore the tradeoff between BC and AC in terms of power consumption and transmission rate, enabling each SU to transmit signal via passive BC and AC alternatively. We propose two problems to maximize the total rate of all SUs under the fixed and dynamic SIC ordering, respectively. The fixed SIC ordering-based problem is to jointly optimize the SUs' reflection coefficients, the transmit power of each SU during AC, and the time allocation for each SU during BC and AC, subject to the energy causality constraint and the PT's transmission rate gain constraint. In addition to pondering the constraints involved in the fixed SIC ordering-based problem, the dynamic SIC ordering-based problem, which is a mixed integer programming one, further considers the SIC ordering constraint. The above two problems are solved by our proposed SCA-based and BCD-based iterative algorithms, respectively. Simulation results demonstrate that: 1) the proposed mutualistic SR system outperforms traditional designs in terms of the rates achieved by SUs under the same constraints; 2) the total rate of all SUs under the dynamic SIC ordering is larger than that of the fixed one when the PT's minimum rate gain is high, and becomes nearly identical when the PT's minimum rate gain is low.