Two-dimensional (2D) palladium ditelluride (PdTe2) and platinum ditelluride (PtTe2) are two Dirac semimetals which demonstrate fascinating quantum properties such as superconductivity, magnetism and topological order, illustrating promising applications in future nanoelectronics and optoelectronics. However, the synthesis of their monolayers is dramatically hindered by strong interlayer coupling and orbital hybridization. In this study, an efficient synthesis method for monolayer PdTe2 and PtTe2 is demonstrated. Taking advantages of the surface reaction, epitaxial growth of large-area and high quality monolayers of PdTe2 and patterned PtTe2 is achieved by direct tellurization of Pd(111) and Pt(111). A well-ordered PtTe2 pattern with Kagome lattice formed by Te vacancy arrays is successfully grown. Moreover, multilayer PtTe2 can be also obtained and potential excitation of Dirac plasmons is observed. The simple and reliable growth procedure of monolayer PdTe2 and patterned PtTe2 gives unprecedented opportunities for investigating new quantum phenomena and facilitating practical applications in optoelectronics.