I've seen 的 used after a verb like this in other sentences. The only thing I could find about 的 after a verb was when it's used with 是.
Here, you could think that "的" converts a verb (i.e. "喝"/drink) into a noun, i.e. something for drinking.
But notice the "的" after "是" is different, it is more of an interjection, and does not have additional meaning.
喝的 is something for drinking, simply some drinks. 的 is something, some stuff, unnamed stuff, something related to.
Chinese is less bound to type of words comparing to English.
大的嗎？ 用的嗎？ 十號的嗎？ 位元堂的嗎？ 他的嗎？
Interestingly, you can replace a verb with an adjective, a noun, or a pronoun. 的 is just something related to a word.