Nitai broke the Danda of Lord Gauranga because He wanted to show the entire world that He won’t let Gaur give danda (punishment) to anyone who takes His shelter. Danda-bhanga means Nitai saves us from Gaur-Krishna’s punishments.
gaura danda kare jadi tumi rakshaa kara
tumi yaare danda kara gaura taara para
(NDM Chapter 4, Shrila Jiva Goswami’s prayer to Nitai)