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We present results from simulating slitless spectroscopic observations with the Nancy Grace Roman Space Telescope's (Roman) Wide-Field Instrument (WFI) P127 prism spanning 0.75 $μm$ to 1.8 $μm$. We quantify the efficiency of recovered Type Ia supernovae (SNe Ia) redshifts, as a function of P127 prism exposure time, to guide planning for future observing programs with the Roman prism. Generating the two-dimensional dispersed images and extracting one-dimensional spectra is done with the slitless spectroscopy package pyLINEAR along with custom-written software. From the analysis of 1698 simulated SN Ia P127 prism spectra, we show the efficiency of recovering SN redshifts to $z\lesssim3.0$, highlighting the exceptional sensitivity of the Roman P127 prism. Redshift recovery is assessed by setting a requirement of $σ_z = (\left|z - z_\mathrm{true} \right|)/(1+z) \leq 0.01$. We find that 3 hr exposures are sufficient for meeting this requirement, for $\gtrsim 50\%$ of the sample of mock SNe Ia at $z\approx2$ and within $\pm5$ days of rest-frame maximum light in the optical. We also show that a 1 hr integration of Roman can achieve the same precision in completeness to a depth of $24.4 \pm 0.06$ AB mag (or $z\lesssim 1$). Implications for cosmological studies with Roman P127 prism spectra of SNe Ia are also discussed.