Is definitively cutting ties with a female colleague who insults the Quran and the Prophet Muhammad, questions the rulings of Sharia, and disputes the history of Islamic conquests considered a correct action?

If the girl you mentioned is in the state you described, of disbelief in Allah, denying His messengers, and fabricating lies against Him, then it is not permissible to show her affection under any circumstances. One should continue to invite her to goodness with wisdom and good admonition as long as there is hope that she might benefit. However, if her disbelief and obstinacy increase, then there is no harm in ceasing to advise her and turning away from her. This might even be more appropriate and a stronger deterrent to her falsehood. It is permissible to be stern in speech with an obstinate person, and this might be the wisdom in her case. As for the verse you referred to, it is: (And when the ignorant address them, they say, "Peace") [Al-Furqan: 63], and it is a Quranic verse in the third person.