How to Grate Fresh Coconut: Wrap the coconut in a clean kitchen towel. Crack the coconut around its equator with a meat mallet or a hammer, and let the liquid drip out into a bowl. Use the mallet to break the coconut into pieces that are small enough to handle. Use a table knife to pry flesh from shell, inserting the knife between shell and flesh and twisting. Grate the coconut on the large holes of a box grater. Grated coconut is best the day you make it; store it in an airtight container to prevent it from drying out.