If it was a well designed bell box then the bell and its battery would not be damaged ( other bits would be ) and the bell would go into tamper and start sounding.
It really is a ladder job. Together with ear defenders and the right tools. If possible have a look at a similar bell box ( at ground level ) so you know which wires to cut as soon as you have the cover off. Knowing which wire to cut before you go up the ladder will shortened the time the bell is ringing rather than trying to work it out at the top of the ladder.
Have identification with you just in case some one calls the police to say a criminal is trying to silence a brglar alarm
