There is no copyright on “Catholic mystic”, but the expression usually refers to Catholics (most often members of religious orders) who were given extraordinary spiritual insights into the mystery of God. Most of these were able of deep contemplative prayer and experienced an extatic unity with God on the one hand, but also the “dark night of the soul” (complete lack of any awareness of the existence of God) on the other. Many had visions and private revelations.
Well known mystics of the Catholic Church were St Teresa of Ávila, St John of the Cross, St Therese of Lisieux, St Catherine of Siena, Bl. Mother Teresa of Calcutta, St Hildegard of Bingen, St Bridget of Sweden, Bl. Anna Katharina Emmerick…
Among those not (or not yet) canonized, Julian of Norwich, Meister Eckhard, Marthe Robin (a stigmatized Frenchwoman) and many more come into mind.