The deformation mechanism of the Ti-6Al-4V (wt.%) alloy with globular structure was studied under conditions of quasi-static and high-strain compression with rates 10−3 s−1 and 2.1–3.3 × 103 s−1, respectively. High-strain compression was conducted using a Split Hopkinson Pressure Bar (SHPB). The details of the deformation mechanism were evaluated based on the analysis of the deformation hardening curves using the strain hardening exponent concept developed for titanium alloys in tension conditions. The used approach allowed us to identify the stages of plastic deformation observed and the controlling phase in deformation of two-phase alloy through the assessment of the strengthening index, n. It has been found that three deformation stages can be identified in quasi-static conditions. However, when the alloy is compressed at a high strain rate, the third deformation stage does not develop due to the high process rate. Further analysis of deformation curves reveals the leading role of the β-phase under the quasi-static conditions and the essential contribution of the second, α-phase, at a high compression rate. The findings on the deformation mechanism based on the analysis of hardening curves were supported by a detailed structural study.