The process is
documented here, but to summarize: fill out and send an INZ 1023 form, together with both the old and new passports.
You have the option to request either a physical label or an eVisa as part of this process. No fee is payable if you request an eVisa, whereas a fee will be charged if you request a physical label.
Having a previous passport invalidated by being cut is unlikely to pose a problem. Yours is not the only country that does this, and INZ would be well aware that some countries do this: in fact, there are some countries that do not return the previous passport at all. If you prefer to err on the side of caution, then you can follow the guidelines for people whose previous passports are not returned to them (or lost/stolen) and submit a cover letter with your application.