It's not that the first one doesn't make any sense at all, but it's not colloquial.
The main reason for this is just that "water" is not typically used with "of" whereas "process" (when used with the definition used here) almost always takes an "of." We would say, for example, that water is in a bottle or from a bottle, not of a bottle.
A secondary point of confusion is that "washing dishes" is often instead called "dishwashing".
By using "washing dishes," you allow for a possible interpretation where "washing" acts as an adjective describing "dishes", but that doesn't make logical sense: What would a "washing dish" even be? A dish that you just clean over and over but never eat off of? The likelihood for confusion about whether a word ending in -ing is a noun or verb or adjective is lower when it follows "process of", though, because the reader/listener will be expecting a verb.