In what contexts would someone say 她说话很刻 (tā shuōhuà hěn kè) ("she's got a sharp tongue")?
To be honest, 她说话很刻 is hard to understand; I think 她说话很刻薄 would be more natural. Basically it means saying something unkind/acerb/acrid etc.

Here's an explanation about 刻薄.


◎ 刻薄 kèbó
(1) [cutting;harsh;caustic;mean;acrimony]∶待人处事挑剔、无情
那个人为人奸狡诡谲,残忍刻薄
刻薄话