In this paper, a microwave photonic (MWP) phase-/delay-tunable mixer with ultralow mixing spurs based on optical single-sideband polarization modulation (OSSB-PolM) is proposed and theoretically investigated which is verified by simulations. In the proposed structure, by passing the OSSB-PolM signal through a polarization controller (PC) and an optical polarizer (Pol.), a carrier-suppressed optical single-sideband (CS-OSSB) modulated signal is generated. In the up-converter mode, optical carrier, intermediate frequency (IF) even- and (4n+3) odd-order sidebands, n is an integer, local oscillator (LO) even- and (4n+1) odd-order sidebands are suppressed without using any optical/electrical filter. Also, in the down-converter mode, optical carrier, radio frequency (RF) and LO even- and (4n+3) odd-order sidebands are suppressed. By beating sidebands of the pure CS-OSSB signal in a photodetector, RF up-converted (or IF down-converted) signal is generated with ultralow mixing spurs. Simulation results show that the sideband suppression ratio (SSR) for both cases of the up-/down-converted signals are >45 dB in the electrical domain. Effects of the phase and power imbalances of the practical non-ideal RF hybrid couplers on the performance of the proposed MWP mixer are investigated. It is shown that with ±3 degrees phase and ±1.5 dB power imbalances, the SSR decreases to 25.6 dB and 15.6 dB, respectively. Closed-form expression for the conversion efficiency is derived which is verified by simulations. Besides, simulations show that the spurious-free dynamic range (SFDR) of the proposed MWP mixer is 117.67 dB.Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2/3</sup> (with −160 dBm/Hz noise floor). In addition, optical frequency conversion and optical phase-shifting functions are combined and a full-range phase-tunable MWP mixer is proposed and investigated. Besides, optical frequency conversion function and optical true-time delay (TTD) are combined and a delay-tunable MWP mixer is introduced and investigated. It can find many applications in MWP systems, such as in MWP TTD beamformers for broadband squint-less array antennas.