Ram pressure stripping has been proven to be effective in shaping galaxy properties in dense environments at low redshift. The availability of Multi Unit Spectroscopic Explorer (MUSE) observations of a sample of distant (z ~ 0.3-0.5) clusters has allowed one to search for galaxies subject to this phenomenon at significant lookback times. In this paper we describe how we discovered and characterized 13 ram-pressure-stripped galaxies in the central regions of two intermediate redshift (z ~ 0.3-0.4) clusters, A2744 and A370, using the MUSE spectrograph. Emission-line properties as well as stellar features have been analyzed to infer the presence of this gas-only stripping mechanism, that produces spectacular ionized gas tails (Hα and even more astonishing [O II](3727, 3729)) departing from the main galaxy body. The inner regions of these two clusters reveal the predominance of such galaxies among blue star-forming cluster members, suggesting that ram pressure stripping was even more effective at intermediate redshift than in today's universe. Interestingly, the resolved [O II]/Hα line ratio in the stripped tails is exceptionally high compared to that in the disks of these galaxies, (which is comparable to that in normal low-z galaxies), suggesting lower gas densities and/or an interaction with the hot surrounding intracluster medium.