Abstract: We study the physical origins of outflowing cold clouds in a sample of 14 low-redshift dwarf (M * ≲ 1010 M ⊙) galaxies from the Cosmic Origins Spectrograph Legacy Archive Spectroscopic SurveY (CLASSY) using Keck/ESI data. Outflows are traced by broad (FWHM  ∼260 km s−1) and very-broad (VB; FWHM ∼1200 km s−1) velocity components in strong emission lines like [O iii] λ5007 and Hα. The maximum velocities ( v max ) of broad components correlate positively with star formation rate, unlike the anticorrelation observed for VB components, and are consistent with superbubble models. In contrast, supernova-driven galactic wind models better reproduce the v max of VB components. Direct radiative cooling from a hot wind significantly underestimates the luminosities of both broad and VB components. A multiphase wind model with turbulent radiative mixing reduces this discrepancy to at least 1 dex for most VB components. Stellar photoionization likely provides additional energy since broad components lie in the starburst locus of excitation diagnostic diagrams. We propose a novel interpretation of outflow origins in star-forming dwarf galaxies—broad components trace expanding superbubble shells, while VB components originate from galactic winds. One-zone photoionization models fail to explain the low-ionization lines ([S ii] and [O i]) of broad components near the maximal starburst regime, which two-zone photoionization models with density-bounded channels instead reproduce. These two-zone models indicate anisotropic leakage of Lyman continuum photons through low-density channels formed by expanding superbubbles. Our study highlights extreme outflows ( v max ≳ 1000 km s − 1 ) in nine out of 14 star-forming dwarf galaxies, comparable to active galactic nucleus–driven winds.