We describe a new method for simulating ionizing radiation and supernova feedback in the analogs of low-redshift galactic disks. In this method, which we call star-forming molecular cloud (SFMC) particles, we use a ray-tracing technique to solve the radiative transfer equation for ultraviolet photons emitted by thousands of distinct particles on the fly. Joined with high numerical resolution of 3.8 pc, the realistic description of stellar feedback helps to self-regulate star formation. This new feedback scheme also enables us to study the escape of ionizing photons from star-forming clumps and from a galaxy, and to examine the evolving environment of star-forming gas clumps. By simulating a galactic disk in a halo of 2.3 $times$ 1011 M ☉, we find that the average escape fraction from all radiating sources on the spiral arms (excluding the central 2.5 kpc) fluctuates between 0.08% and 5.9% during a ∼20 Myr period with a mean value of 1.1%. The flux of escaped photons from these sources is not strongly beamed, but manifests a large opening angle of more than 60° from the galactic pole. Further, we investigate the escape fraction per SFMC particle, f esc(i), and how it evolves as the particle ages. We discover that the average escape fraction f esc is dominated by a small number of SFMC particles with high f esc(i). On average, the escape fraction from an SFMC particle rises from 0.27% at its birth to 2.1% at the end of a particle lifetime, 6 Myr. This is because SFMC particles drift away from the dense gas clumps in which they were born, and because the gas around the star-forming clumps is dispersed by ionizing radiation and supernova feedback. The framework established in this study brings deeper insight into the physics of photon escape fraction from an individual star-forming clump and from a galactic disk.