The main advantage of numerical methods such as Finite Elements (FE) in modeling surface acoustic wave (SAW) devices lies in their ability to model devices involving complicated transducer geometries. We present a 3-D finite element model of a novel hexagonal SAW biosensor based on LiTaO3 substrate. This SAW biosensor involves the use of one delay path for biological species detection whereas the other delay paths are used to simultaneously remove the non-specifically bound proteins using the acoustic streaming phenomenon, thus eliminating biofouling issues associated with other biosensors. Prior to this biosensor fabrication on any piezoelectric substrate, it is important to establish the type of waves that are generated along the various delay paths. The choice of a delay path for sensing and simultaneous cleaning application depends on the propagation characteristics of the wave generated along the crystal cut and orientation corresponding to that delay path. The frequency response as well as wave propagation characteristics along the delay path corresponding to crystal orientation with on-axis propagation along 36deg YX LiTaO3 substrate are analyzed using a coupled field FE model. Similar analysis is extended to the off-axis propagation directions corresponding to Euler rotations by 60deg and -60deg along the x-z plane. Our findings indicate that the on-axis direction with a significant surface shear horizontal (SH) component should be employed for biological species detection whereas the off-axis directions having mixed modes with a dominant Rayleigh wave component are most suitable for simultaneous cleaning or removal application.