A machine for working glass slabs includes a supporting structure, a slab grinding section having grinding heads, a conveyor assembly adapted to move the glass slab, and a slab drilling section having a conveyor adjacent to the conveyor assembly. The slab grinding section has suckers for keeping the glass slab next to a working plane spaced and/or offset with respect to the advancement plane, and a computerized numeric control assembly to perform workings on the glass slab.

A machine (10) and a process are described, for working glass slabs (21), the machine (10) comprising: a supporting structure (11); a slab grinding section (12) comprising grinding heads (64), and a conveyor assembly (18) having dragging means (24) adapted to move the glass slab (21); a slab drilling section (14) comprising a conveyor (31) adjacent to the conveyor assembly (18); the slab grinding section (12) further comprises retaining means (45) for keeping the glass slab (21) next to a working plane (25) spaced and/or offset with respect to the advancement plane (23); and a computerized numeric control assembly (68) for perform workings on the glass slab (21).