The supercurrent diode effect (SDE), characterized by unequal critical currents in opposite directions, has been observed with or without magnetic fields, yet mechanisms enabling zero-field SDE without explicit symmetry breaking remain underexplored. Here we investigate a Josephson junction with strong electron-electron interaction modeled by a Hubbard U term and an odd number of electrons. We find that strong correlations induce spontaneous breaking of time-reversal and mirror symmetries, forming a ϕ-junction with degenerate energy minima at ±ϕ, resulting in zero-field Josephson diode effect (JDE) without magnetic order. Spin-orbit coupling breaks SU(2) symmetry but does not determine diode polarity, contrasting with magneto-chiral mechanisms. We further show that applying a tiny Zeeman field enables controllable JDE with sizable efficiency due to the enhancement by the strong magnetic correlation, and the JDE strength peaks when the field induces a level-crossing transition. These findings establish strong electron correlation as a distinct mechanism for nonreciprocal superconducting transport, broadening the understanding of SDE origins.