We report on three-dimensional (3D) magnetohydrodynamic (MHD) simulations of recurrent eruptions in emerging flux regions. We find that reconnection of sheared field lines, along the polarity inversion line of an emerging bipolar region, leads to the formation of a new magnetic structure, which adopts the shape of a magnetic flux rope (FR) during its rising motion. Initially, the FR undergoes a slow-rise phase and, eventually, it experiences a fast-rise phase and ejective eruption toward the outer solar atmosphere. In total, four eruptions occur during the evolution of the system. For the first eruption, our analysis indicates that the torus instability initiates the eruption and that tether-cutting reconnection of the field lines, which envelop the FR, triggers the rapid acceleration of the eruptive field. For the following eruptions, we conjecture that it is the interplay between tether-cutting reconnection and torus instability that causes the onset of the various phases. We show the 3D shape of the erupting fields, focusing more on how magnetic field lines reconnect during the eruptions. We find that when the envelope field lines reconnect mainly with themselves, hot and dense plasma is transferred closer to the core of the erupting FR.The same area appears to be cooler and less dense when the envelope field lines reconnect with neighboring sheared field lines. The plasma density and temperature distribution, together with the rising speeds, energies, and size of the erupting fields, indicate that they may account for small-scale (mini) coronal mass ejections.