An analysis leveraging 170 optical spectra of 35 stripped-envelope (SE) core-collapse supernovae (SNe) observed by the Carnegie Supernova Project I and published in a companion paper is presented. Mean template spectra were constructed for the SNe IIb, Ib, and Ic subtypes, and parent ions associated with designated spectral features are identified with the aid of the spectral synthesis code SYNAPPS. Our modeled mean spectra suggest the ~6150 Å feature in SNe IIb may have an underlying contribution due to silicon, while the same feature in some SNe Ib may have an underlying contribution due to hydrogen. Standard spectral line diagnostics consisting of pseudo-equivalent widths (pEWs) and blue-shifted Doppler velocity were measured for each of the spectral features. Correlation matrices and rolling mean values of both spectral diagnostics were constructed. A principle component analysis (PCA) was applied to various wavelength ranges of the entire dataset and suggests clear separation among the different SE SN subtypes, which follows from trends previously identified in the literature. In addition, our findings reveal the presence of two SNe IIb subtypes, a select number of SNe Ib displaying signatures of weak, high-velocity hydrogen, and a single SN Ic with evidence of weak helium features. Our PCA results can be leveraged to obtain robust subtyping of SE SNe based on a single spectrum taken during the so-called photospheric phase, separating SNe IIb from SNe Ib with ~80% completion.