We study the phase-controlled transmission properties in a compound system consisting of a three-dimensional copper cavity and an yttrium-iron-garnet (YIG) sphere. By tuning the relative phase of the magnon pumping and cavity-probe tones, constructive and destructive interferences occur periodically, which strongly modify both the cavity-field transmission spectra and the group delay of light. Moreover, the tunable amplitude ratio between pump-probe tones allows us to further improve the signal absorption or amplification, accompanied by either significantly enhanced optical advance or delay. Both the phase and amplitude ratio can be used to realize in situ tunable and switchable fast-slow light. The tunable phase and amplitude ratio lead to the zero reflection of the transmitted light and an abrupt fast-slow light transition. Our results confirm that direct magnon pumping through the coupling loops provides a versatile route to achieve controllable signal transmission, storage, and communication, which can be further expanded to the quantum regime, realizing coherent-state processing or quantum-limited precise measurements.