We present a UV spectroscopic study of ionized outflows in 21 active galactic nuclei (AGN), observed with theHubbleSpace Telescope (HST). The targets of the Supermassive Black Hole Winds in X-rays (SUBWAYS) sample were selected with the aim to probe the parameter space of the underexplored AGN between the local Seyfert galaxies and the luminous quasars at high redshifts. Our targets, spanning redshifts of 0.1–0.4 and bolometric luminosities (L_bol) of 10⁴⁵–10⁴⁶erg s⁻¹, have been observed with a large multi-wavelength campaign usingXMM-Newton,NuSTAR, and HST. Here, we model the UV spectra and look for different types of AGN outflows that may produce either narrow or broad UV absorption features. We examine the relations between the observed UV outflows and other properties of the AGN. We find that 60% of our targets show a presence of outflowing H Iabsorption, while 40% exhibit ionized outflows seen as absorption by either C IV, N V, or O VI. This is comparable to the occurrence of ionized outflows seen in the local Seyfert galaxies. All UV absorption lines in the sample are relatively narrow, with outflow velocities reaching up to −3300 km s⁻¹. We did not detect any UV counterparts to the X-ray ultra-fast outflows (UFOs), most likely due to their being too highly ionized to produce significant UV absorption. However, all SUBWAYS targets with an X-ray UFO that have HST data demonstrate the presence of UV outflows at lower velocities. We find significant correlations between the column density (N) of the UV ions andL_bolof the AGN, withN_{H I}decreasing withL_bol, whileN_{O VI}is increasing withL_bol. This is likely to be a photoionization effect, where toward higher AGN luminosities, the wind becomes more ionized, resulting in less absorption by neutral or low-ionization ions and more absorption by high-ionization ions. In addition, we find thatNof the UV ions decreases as their outflow velocity increases. This may be explained by a mechanical power that is evacuating the UV-absorbing medium. Our observed relations are consistent with multiphase AGN feeding and feedback simulations indicating that a combination of both radiative and mechanical processes are in play.