  We present a method for isolating a clean sample of red giant stars in the
outerregions of the Andromeda spiral galaxy (M31) from an ongoing spectroscopic
survey using the DEIMOS instrument on the Keck 10-m telescope. The survey aims
to study the kinematics, global structure, substructure, and metallicity of
M31's halo. Although most of our spectroscopic targets were photometrically
screened to reject foreground Milky Way dwarf star contaminants, the latter
class of objects still constitutes a substantial fraction of the observed
spectra in the sparse outer halo. Our likelihood-based method for isolating M31
red giants uses five criteria: (1) radial velocity, (2) photometry in the
intermediate-width DDO51 band to measure the strength of the MgH/Mgb absorption
features, (3) strength of the Na I 8190A absorption line doublet, (4) location
within an (I, V-I) color-magnitude diagram, and (5) comparison of photometric
(CMD-based) versus spectroscopic (Ca II 8500A triplet-based) metallicity
estimates. We also discuss K I and TiO diagnostics for giant/dwarf separation
that might be useful in future analyses. Training sets consisting of definite
M31 red giants and Galactic dwarf stars are used to derive empirical
probabilitydistribution functions for each diagnostic. These functions are used
to calculate the likelihood that a given star is a red giant in M31 versus a
Milky Way dwarf. By applying this diagnostic method to our spectroscopic data
set, we isolate 40 M31 red giants beyond a projected distance of R = 60 kpc
from the galaxy's center, including three out at R ~ 165 kpc. The ability to
identify individual M31 red giants gives us an unprecedented level of
sensitivity in studying the properties of the galaxy's outer halo.
