  SN H0pe is a triply imaged supernova (SN) at redshift $z=1.78$ discovered
using the James Webb Space Telescope (JWST). In order to classify the SN
spectroscopically and measure the relative time delays of its three images
(designated A, B, and C), we acquired NIRSpec follow-up spectroscopy spanning
0.6 to 5 microns. From the high signal-to-noise spectra of the two bright
images B and C, we first classify the SN, whose spectra most closely match
those of SN 1994D and SN 2013dy, as a Type Ia SN. We identify prominent
blueshifted absorption features corresponding to Si II $\lambda6355$ and Ca II
H $\lambda3970$ and K $\lambda3935$. We next measure the absolute phases of the
three images from our spectra, which allows us to constrain their relative time
delays. The absolute phases of the three images, determined by fitting the
three spectra to Hsiao07 SN templates, are $6.5_{-1.8}^{+2.4}$d,
$24.3_{-3.9}^{+3.9}$d, and $50.6_{-15.3}^{+16.1}$d for the brightest to
faintest images. These correspond to relative time delays between Image A and
Image B and between Image B and Image C of $-122.3_{-43.8}^{+43.7}$d and
$49.3_{-14.7}^{+12.2}$d, respectively. The SALT3-NIR model yields phases and
time delays consistent with these values. After unblinding, we additionally
explored the effect of using Hsiao07 template spectra for simulations through
eighty instead of sixty days past maximum, and found a small (11.5 and 1.0
days, respectively) yet statistically insignificant ($\sim$0.25$\sigma$ and
$\sim$0.1$\sigma$) effect on the inferred image delays.
