Deformational cutting can be used for manufacturing meshes. A metal or polymer sheet with a thickness of 0.2-0.8 mm is used as blanks when producing meshes. The sheet is tightened on a cylindrical fixture, then finned by the deformational cutting method on both sides without separating chips. The finning on the second side is made perpendicular or at an angle to the direction of fins on the first side. The cut depth at finning both sides of the sheet is more than half of its thickness, which ensures the connection of interfin gaps on the opposite sides of the sheet. On the lathe by the deformational cutting method from metal and polymer (PET, Teflon) sheets, samples of meshes with cells from 20 microns were obtained. Finning on the opposite sides of the sheet not in perpendicular directions leads to the possibility of mesh stretching. In this work, the two-sided finning of thin-sheet titanium blanks with different finning directions of the opposite sides and variation of deformational cutting parameters is studied. The analysis of the stretching mechanics for obtaining rhombic, hexagonal, and parallelogram shapes of cells is carried out. The range of finning pitches and crossing angles that ensure the stability of the deformational cutting process and mesh stretching is established. The shape of the cell is mainly influenced by the length of the fin connection obtained on the opposite sides of the sheet. Increasing the connection length with a decrease in the intersection angle leads to the transition of the cell shape from rhombic to hexagonal. A parallelogram cell obtained in stretching is characteristic of the fins of opposite sides with differences in bending strength.