The following mean all the same to me, but the bold された strongly suggests 被害/迷惑の受け身, so that 2 and 3 sound more like the speaker thinking she is damaged by being abandoned while 1 more neutrally states she was abandoned and that in a bad way. But these are a bit 'theoretical', I don't think they are really distinguished consciously.
Note: 彼女はひどい捨て方をした means she is the one who abandoned.
Grammatically, one thing I noticed in a dictionary is that 方 can mean
- ２ 動詞の連用形や動作性の漢語名詞に付いて、…すること、の意を表す。「打ち―やめ」「調査―を依頼される」
The 方 retains some meaning of way, but here it functions more as a nominalizer, so the above are roughly the same as the following (unnatural) sentences
which roughly correspond to
- She did (went through) the experience of being abandoned in a horrible way.
- The experience of being abandoned in a horrible way was done to her.
- She was done (a victim of) the act of abandoning in a horrible way.
I think ultimately all these work somehow by vagueness of 方（こと）・する.
Another thing to consider is the fact that generally there is no straightforward translation for in adj. way.
For example, it is not possible to translate he abandoned her in a cruel way into かれはadjなやりかたで/advで彼女を捨てた. 残酷に won't sound idiomatic here. (I mean this only generally. In specific cases, there could be straightforward translations. E.g. in a simple way = 単純に).