Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in a counter-rotating two-color elliptically polarized (TCEP) field are investigated by using a three-dimensional classical ensemble model. The numerical results show that the correlated momentum distribution of electron pairs in the x-axis direction evolves from a V-shaped structure in the first quadrant at the low intensity, to an arc-shaped structure mainly located in the second and fourth quadrants at moderate intensity, finally to a distribution near the origin located in the first quadrant in the high intensity. With the laser intensity increasing, the dominant correlation behavior evolves from correlation to anti-correlation and finally reverts back to correlation. The combined electric field traces out a trefoil pattern, i.e. the waveform in a period shows three leaves in different directions. Each leaf is called a lobe. The electric field recursively evolves from lobe 1 to lobe 2 and to lobe 3. Unlike the counter-rotating two-color circularly polarized fields, the combined fields from two elliptical fields do not have the spatial symmetry. Amplitudes of the three field lobes and the angles between them are different. Furthermore, the back analysis of NSDI trajectories shows that the single ionization in NSDI events mainly occurs in lobe 1 and lobe 3, and the contribution from lobe 1 increases and that from lobe 3 decreases with the increase of the intensity. Correspondingly, the free electrons mainly return to the parent ion from 20° and 175°. With the laser intensity increasing, the electrons returning from 20° gradually increase and those returning from 175° gradually decrease. In order to further understand the correlation behaviors of electron pairs in the x-axis direction, the NSDI events triggered off by single ionization from different lobes are separately discussed. With the increase of laser intensity the correlation behavior of NSDI events triggered off by single ionization from field lobe 1 evolves from anti-correlation behavior to correlation behavior, but the correlation behavior of NSDI events induced by single ionization from field lobe 3 evolves from correlation behavior to anti-correlation behavior. With the laser intensity increasing, the NSDI events induced by single ionization from field lobe 1 increase gradually, but those from field lobe 3 decrease. This results in that the total dominant correlation behavior evolves from correlation to anti-correlation and finally reverts back to correlation as the laser intensity increases.