A Serrodyne microwave frequency translator implemented using a microwave photonic technique is presented. It is based on two dual-drive Mach Zehnder modulators connected in parallel where one of the modulators is operated as an optical phase modulator driven by a sawtooth wave. It is capable of simultaneously shifting the frequency and phase of an input microwave signal. The frequency translator is designed to largely suppress the undesired carrier and sidebands and to minimise the frequency translation loss. Results on the frequency translator demonstrate -1 MHz to 1 MHz frequency translation of multiple microwave signals with a large spurious suppression ratio of 34 to 41 dB and a wide bandwidth of 2 to 18 GHz. Simultaneous frequency and phase shifting operation is also demonstrated.