We demonstrate and study a microcell microwave atomic clock based on optical-microwave double resonance (DR) interrogation operated in a pulsed Ramsey scheme, called the mu POP clock, based on a microfabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 4-5 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the mu POP clock shows that the pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1 x 10(-11) tau(-1/2) and reaching the <= 2 x 10(-12) level at timescales of 1000 s to one day. The short-term instability budget established for the mu POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the mu POP clock, which opens perspectives for further improvements of long-term clock stability, in view of future generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.