A glass material cutting apparatus for cutting a glass material discharged from a glass material reservoir into a glass gob of a predetermined size by left and right cutting blades (91, 92) opposed to each other, comprising: a horizontal movement mechanism for translating said cutting blades (91, 92) close to or away from each other in a horizontal direction, and an upward and downward movement mechanism for moving said horizontal movement mechanism in an upward and downward direction, said cutting blades (91, 92) being movable in a forward direction from respective stand-by positions (P, P1) and in a downward direction to cut the glass material, and thereafter, in a further downward direction and in a backward direction, and thereafter, in an upward direction to return back to said stand-by positions (P, P1), wherein said horizontal movement mechanism and said upward and downward movement mechanism are driven by a single driving device mounted on a base plate, said glass material cutting apparatus further comprising: left and right operating members (55, 56) which are rotatable by said single driving device, left and right cam members (61, 62) which are rotatable together with said operating members (55, 56) and which have first cam portions (65, 66) and second cam portions (67, 68), respectively, an elevator member which has first engagement portions (71, 72) which are engaged with the first cam portions (65, 66) of said cam members (61, 62) and which are moved up and down along a vertical rail provided on said base plate, in accordance with a rotation of said cam members (61, 62), left and right supporting members (81, 82) which have second engagement portions (83, 84) which are engaged with the second cam portions (67, 68) of said cam members (61, 62) and which are moved laterally close to or away from each other along a lateral rail provided on said elevator member, in accordance with a rotation of said cam members (61, 62), and said left and right cutting blades (91, 92) which are provided on said supporting members (81, 82) and are opposed to each other. a horizontal movement mechanism for translating said cutting blades (91, 92) close to or away from each other in a horizontal direction, and an upward and downward movement mechanism for moving said horizontal movement mechanism in an upward and downward direction, said cutting blades (91, 92) being movable in a forward direction from respective stand-by positions (P, P1) and in a downward direction to cut the glass material, and thereafter, in a further downward direction and in a backward direction, and thereafter, in an upward direction to return back to said stand-by positions (P, P1), wherein said horizontal movement mechanism and said upward and downward movement mechanism are driven by a single driving device mounted on a base plate, left and right operating members (55, 56) which are rotatable by said single driving device, left and right cam members (61, 62) which are rotatable together with said operating members (55, 56) and which have first cam portions (65, 66) and second cam portions (67, 68), respectively, an elevator member which has first engagement portions (71, 72) which are engaged with the first cam portions (65, 66) of said cam members (61, 62) and which are moved up and down along a vertical rail provided on said base plate, in accordance with a rotation of said cam members (61, 62), left and right supporting members (81, 82) which have second engagement portions (83, 84) which are engaged with the second cam portions (67, 68) of said cam members (61, 62) and which are moved laterally close to or away from each other along a lateral rail provided on said elevator member, in accordance with a rotation of said cam members (61, 62), and said left and right cutting blades (91, 92) which are provided on said supporting members (81, 82) and are opposed to each other.