A method of cutting a glass sheet that has been thermally or chemically strengthened along a predetermined line, axis, or direction with high speed and with minimum damage on the cut edges. The strengthened glass sheet may be an aluminoborosilicate glass material having at least one alkali metal oxide modifier, and the ratio Al 2 ⁢ O 3 ⁡ ( mol ⁢ ⁢ % ) + B 2 ⁢ O 3 ⁡ ( mol ⁢ ⁢ % ) ∑ ⁢ modifiers ⁢ ⁢ ( mol ⁢ ⁢ % ) > 1. At least one damage line is formed within the strengthened glass sheet. The at least one damage line is formed outside the strengthened compressive stress surface layers and within the tensile stress layer of the strengthened glass sheet. The at least one damage line may be formed by laser treatment. A crack is initiated in the strengthened glass sheet and propagated along the at least one damage line to separate the strengthened glass sheet along the predetermined line, axis, or direction into at least two pieces.