Method for manufacturing a CMC, i.e. ceramic matrix composite material, part provided with at least one cutout, as well as to such a CMC part provided with at least one cutout, the method comprising the following steps:



providing (E1) a fibrous reinforcement (10),
forming (E2′) a cavity in a portion of the fibrous reinforcement (10),
injecting (E3) a slip comprising at least a ceramic powder and a solvent, the slip being injected so as to impregnate the fibrous reinforcement (10′) and to fill the cavity of the fibrous reinforcement (10′),
drying (E4) the obtained assembly,
carrying out a densification (E6) by infiltration of a liquid densification material and solidification of said densification material,
machining (E7) at least one cutout in the obtained blank (30) within the volume corresponding to the cavity of the fibrous reinforcement (10).