If you are looking for a DIY way to remove an old Nivito kitchen faucet, you've come to the right place. There are several things that you need to do in order to remove the faucet and save yourself some money. You should first remove the mounting hardware that holds the faucet to the sink. Once this has been removed, you can simply lift the faucet out of the sink holes. Alternatively, you can call a local handyman to help you with this.