Saucy has a totally different meaning. When I describe food having too much sauce, I would like to use an adjective, however salty is not really applicable here.
I'm not sure what the objection to using saucy is all about. Merriam-Webster says:
1: served with or having the consistency of sauce
2a : impertinently bold and impudent
b : amusingly forward and flippant : irrepressible
3: smart, trim <a saucy little hat>
The very first definition is exactly the meaning you are looking for. Sure, the word has other meanings, but most words have multiple meanings. If your food is too saucy, then just say so.
How about "over-sauced"?
While the suggestion "swimming in sauce" as suggested by nico is the probably the most idiomatic option, it's colloquial and might not be the best choice if you were speaking, say, formally in a kitchen or in a restaurant review.
As mentioned above also, "saucy" is an old term meaning "pert" or "impudent." Yet, the primary definition offered by Merriam-Websters is "served with or having the consistency of sauce." So given these prior meanings, whatever solution devised will be a nonce coinage.
There isn't a word for that specifically. However, in some cases you might describe something as "runny" if it has too much liquid and isn't solid enough.
If you are just looking for a contraction of "was made with too much sauce", you could describe it as "over sauced" although this is not an everyday phrase (we are simply using the prefix "over" as it can be used with any verb) and may sound a bit pretentious.
From a practical point of view, within the context of food, you will be understood if you just say "too saucy", although it's not dictionary-correct.
If I were served a dish with a sauce that had far too much sauce, I would call it "soupy". As in, there's so much sauce that it may as well be a soup.