I'm not sure this has to do with English Language & Usage, but more the fact that watermelons are relatively large, at least compared to mangoes and oranges. A mango or an orange would feed a single person, but a single watermelon can feed a whole family. Thus, watermelon gets used in the mass sense because you would use at most one watermelon in a fruit salad, unless you were making a really large one for a catered event, while mangoes and oranges are count and plural because you would need at least two to complement the watermelon.
Now, the context is a fruit salad, so it would be understood that each of these fruits would be cut up (or, in the case of the oranges, peeled apart) and the pieces then mixed into the salad, but the sentence by itself is ... not ungrammatical, but grammatically suspect, as it lacks parallelism and that has implications of its own. Namely: the mangoes and oranges are whole, but the watermelon isn't, which is not the case. The "best" way to rephrase this would be
"I am mixing mango slices, watermelon cubes and orange wedges"
but that implies a particular way you're cutting up the fruit, adding context that the original doesn't have and that might be unwanted.
But the context is given, and that overrides the implications of which fruits are whole. The implication that wouldn't be overridden is how much watermelon is used: If it's count, it must be singular, and even then it might still be too much. Letting the watermelon be mass while the mangoes and oranges are count allows the listener to understand that "just enough" of each fruit was used, without the speaker specifying anything else.