Among the many writings of the 12th-century English monk/canon Alexander Neckam, he describes what you might find on a seagoing ship. He mentions that you need shrouds and stays to support the mast, but also that the ship should be "equipped with weapons, namely, a hatchet, so that the mast can be cut when a storm is brewing" (the Latin says "...securi, ut malus abscindi possit tempestate emergente" - there's a longer translation in Google Books here if you want to see it in context).
The "emergente" (brewing storm) makes it clear that he thinks this is a precautionary measure. But as a sailor myself, that seems suspicious to me. Having a bare mast up with no sails isn't too dangerous except in the worst storms, and what happens when the storm abates and you have no mast? Are you left just paddling? So I suspect that Neckam (who had made a sea crossing to France, but was hardly an expert) had just misunderstood, and the hatchet was actually meant for cutting the ropes that secured the mast, if the mast was broken down during a storm and needed to be cut free. That's certainly what yachts(wo)men would do today.
But am I wrong? Might sailors really have cut down their mast in preparation for a storm? I'd be interested in your thoughts.
Medieval ships didn't have multi-part masts like early modern ships did -- their masts were very large and made of several sticks bound together, to hold the weight of a very heavy yard and sail. It's not until the 1600s that we get masts made in parts, in the way that you might think of when you think of a classic man-of-war, where you have a mast stepped at the keel of a ship, then a topmast over it, then a topgallant mast over it and so forth -- this can be struck down in case of a storm, but early medieval ships didn't have any such thing.
Apologies for the potato quality of these scans -- I don't have a book scanner where I work -- but these are depictions of medieval carracks with this type of mast. It needed to be that large to support the extremely large yards and sails that medieval ships carried -- before the sails on a given mast are broken up into courses, topsails, etc. they had to get all their motive power from one yard and sail per mast. It certainly wouldn't do to cut your mast down for a light rain shower, but that amount of top-hamper would be problematic in a serious storm, and mariners would absolutely cut it down if they were otherwise threatened by a wreck.
Scans are from Rodger, The Safeguard of the Sea (1998 edition)