For every ton of waste recycled, a city avoids paying for its disposal, which, in parts of New York, amounts to saving of more than ＄100 per ton.
为了理解，暂去掉地点状语 in parts of New York。
For every ton of waste recycled, a city avoids paying for its disposal, which amounts to saving of more than ＄100 per ton.
which amounts to saving of more than ＄100 per ton，这是一个非限制性定语从句。which 指前文整个意思，而不是指某个词语，更不是指its disposal（处理）。所以，第二个翻译正确。
amounts to 是个短语动词，意为“等于；相当于；等同于”，其主语就是 which。网友怎么会理解成副词呢？

【翻译】每回收一吨垃圾，城市就避免了为处理垃圾支付费用，在纽约的部分地区，此举相当于每吨可节省100美元以上。