We study the clustering properties of z~5.7 Lyman-alpha emitters (LAEs) in a cosmological reionization simulation with a full Lya radiative transfer calculation. Lya radiative transfer substantially modifies the intrinsic Lya emission properties, compared to observed ones, depending on the density and velocity structure environment around the Lya emitting galaxy. This environment-dependent Lya selection introduces new features in LAE clustering, suppressing (enhancing) the line-of-sight (transverse) density fluctuations and giving rise to scale-dependent galaxy bias. In real space, the contours of the three-dimensional two-point correlation function of LAEs appear to be prominently elongated along the line of sight on large scales, an effect that is opposite to and much stronger than the linear redshift-space distortion effect. The projected two-point correlation function is greatly enhanced in amplitude by a factor of up to a few, compared to the case without the environment dependent selection effect. The new features in LAE clustering can be understood with a simple, physically motivated model, where Lya selection depends on matter density, velocity, and their gradients. We discuss the implications and consequences of the effects on galaxy clustering from Lya selection in interpreting clustering measurements and in constraining cosmology and reionization from LAEs.