We report an extensive search for Lyα emitters (LAEs) at z = 6.5 in the Subaru Deep Field (SDF). We carried out spectroscopic observations with Subaru/Keck to identify LAEs at z = 6.5 that were selected by narrow-band excess at 920nm. We have identified eight new LAEs based on their significantly asymmetric Lyα emission profiles. This increases the sample of spectroscopically confirmed z = 6.5 LAEs in the SDF to 17. Based on this spectroscopic sample of 17, complemented by a photometric sample of 58 LAEs, we have derived a more accurate Lyα luminosity function (LF) of LAEs at z = 6.5, which reveals an apparent deficit at the bright end, of ∼0.75 mag fainter L*, compared with that observed at z = 5.7. The difference has 3σ significance, which is reduced to 2σ when cosmic variance is taken into account. Several LAEs with high Lyα luminosity have been actually identified by spectroscopy at z<5.7, while our LAE sample at z = 6.5 has no confirmed object having such a high Lyα luminosity. The LF of the rest UV continuum, which is not sensitive to neutral IGM, of our LAE sample has almost the same as those of LAEs at z = 5.7 and i-dropouts at z≃6, even at their bright ends. This result may imply that the reionization of the universe has not been completed at z = 6.5. The decline of the Lyα LF implies the cosmic neutral fraction xHI=0.45 based on a theoretical IGM model, although this predicted value is strongly model dependent. The spatial distribution of our LAE sample was found to be homogeneous over the field, based on three independent methods to quantify the clustering strength. The composite spectrum of our LAE sample clearly reveals an asymmetric Lyα profile with an extended red wing, which can be explained by either a galactic wind model composed of double Gaussian profiles, or by a reionization model expected from the damping wing profile. Although our result has uncertainties in LAE evolution and large cosmic variance, it can be interpreted that LAEs at z = 6.5 are at the end of the reionization epoch.