This study presents a Microwave Photonic mixer with the function of frequency up/down conversion and full range phase shift. In the proposed scheme, a radio frequency (RF) signal and a local oscillator (LO) drive two dual-parallel Mach-Zehnder modulators (DPMZM), respectively. By establishing the specific bias voltage of two DPMZMs, this scheme can implement the carrier suppressed single sideband (CS-SSB) modulation and 2nd-order single sideband modulation. This study theoretically analyzes and demonstrates the proposed scheme. By changing the DC voltage of PM, we can achieve a continuous full range phase shift, and the phase deviation of the generated signal is less than 1 degree. The signal processor provides a compact alternative for the application including Radio over Fiber (ROF) system and phased-array beamforming since it can realize both frequency conversion and phase shift.