We analyze data cubes of over 60 emission lines in the HH 32 stellar jet acquired with the Keck Cosmic Web Imager (KCWI). The data cover the less explored blue portion of the spectrum between 3586 and 6351 Å and have both high spectral (R ~ 10,000) and spatial (lesssim1'') resolution. The study includes all three major ionization states of oxygen, three Balmer lines, multiple lines of Fe ii and Fe iii, and the first data cubes ever acquired for important unblended diagnostic lines such as He ii λ4686, Ca i λ3933, and Mg i] λ4571. The data cubes generally sort according to excitation and have a relatively continuous progression from the highest-excitation ions (He ii, O iii) through the intermediate-excitation ions (O i and H i) to the lowest-excitation ions (Ca ii and Mg i). Merging the KCWI cubes with Hubble Space Telescope images leads to several new insights about the flow, including evidence for bow shocks, partial bow shocks, spur shocks, Mach disks, jet deflection shocks, a wiggling jet, and potential shock precursors. The most surprising result is that one of the velocity components of Fe ii in the Mach disk suddenly increases in flux relative to other lines by a factor of two, implying that the Mach disk vaporizes dust in the jet. Hence, jets must accelerate or entrain dust to speeds of over 300 km s−1 without destroying the grains.