Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
There is no objection to a Muslim woman cutting part of her hair as long as she does not do so in imitation of disbelieving or dissolute women.
Muslim reported that "The wives of the Prophet (Sallallahu Alaihi wa Sallam) used to take some of their hair until it becomes short like Wafra (short hair)."
However, if shortening the hair is in imitation of disbelieving or dissolute women or if it is in imitation of men then it is forbidden. "The Prophet (Sallallahu Alaihi wa Sallam) cursed the men who imitate women and the women who imitate men." [Reported by Imam Al Bukhari]
Allah knows best.