To easily position a cutting device body in a desktop cutting device for cutting a cut material loaded on a table with a rotary cutting tool moving downward, when tilting the cutting device body leftward or rightward and executing oblique cutting, for example, at a 22.5 tilted position and a 33.9 tilted position which are difficult positions for a conventional cutting device capable of positioning at a right angle cutting position and a 45 tilted position but hardly capable of positioning at other tilting angles.

A positive stop mechanism capable of positioning at a certain tilting angle with one operation is adopted. In addition to a right angle positioning lever 31, the positive stop mechanism includes a positioning pin 41 movable between a locking position and an unlocking position by a rotation operation of a switch lever 45. The positioning pin 41 is moved to the locking position and inserted to positioning holes 50 (51R, 52R, 51L, 52L) at a tilting base part side.