
It depends on the context. If it is a general statement not referrring to a particular watermelon, "watermelon" is OK. "a watermelon" and "watermelons" would also fit into this category.
eg. You need a sharp knife to cut (a) watermelon/watermelons.
If I'm referring to one that is near me which I'm going to cut up for those present at the meal, it would need to "the watermelon".

http://www.oxfordlearnersdictio...ish/watermelon
Watermelon is both a countable noun and an uncountable noun.
One webpage explains that if the fruit it cut up it is uncountable, but before it's cut, it's countable. I think that's how I use the word.
In googlefight, ...
"cut watermelon" beats "cut the watermelon."
"cut a watermelon" beats "cut watermelon"
"cut watermelon" vs. "cut the watermelon"
http://googlefight.com/%22cut+w...ermelon%22.php
"cut watermelon" vs. "cut a watermelon"
http://googlefight.com/%22cut+w...ermelon%22.php

use of "cut watermelon"
Awesome way to cut watermelon.
https://www.youtube.com/watch?v=bKs2QU2Iyk4
Interestingly, despite the title, the man says "I'm going to show you ... how to cut a watermelon" at the start of the video.
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This sentence was initially added as a translation of sentence #4350216
added by marllboro06, July 8, 2015
linked by marllboro06, July 8, 2015
edited by marllboro06, July 10, 2015
linked by vertigo93, July 27, 2015
linked by MarijnKp, May 9, 2019