The invention discloses an MXene two-dimensional material and a Cu/MXene catalyst, and preparation methods and application thereof. The preparation method of the MXene two-dimensional material comprises the following steps: subjecting a uniformly-mixed reaction system containing lithium fluoride, acid and an Mxene precursor to a reaction, oscillating a mixture of a reaction product and water by adopting a mechanical oscillation technology, and carrying out ultrasonic treatment to obtain the MXene two-dimensional material. The invention also discloses the preparation method of the Cu/MXene catalyst. The preparation method of the Cu/MXene catalyst comprises the following steps: carrying out a mixed reaction on a copper source and an MXene two-dimensional material solution, carrying out centrifugal treatment, and drying a solid obtained after centrifugation so as to obtain the Cu/MXene catalyst. The two-dimensional catalyst material of the Cu/MXene catalyst has the characteristics of highdispersity and accurate control of the site position of an active component, and has good application prospects in the fields of a Sonogashira coupling reaction, reduction of 4-NP and the like.