Matthew Hocter from Albumism described "Cuts Both Ways" as a "heartbreakingly beautiful song of love lost", and picked it as one of the "highlights" of the album of same name.[6] Bill Coleman from Billboard viewed it as a "trademark-styled ballad, highlighted by lovely acoustic guitars and affecting vocals."[7] David Giles from Music Week deemed it a "big ballad". He added, "Cliched lyrics aside; its acoustic guitar is undeniably pleasant and her voice is left attractively uncluttered, Carpenters style."[8] A reviewer from The Network Forty noted that "shifting gears from power ballad to folk to Latin, this single has a deeper message, both musically and lyrically, than you might expect."[9] Pop Rescue wrote that "this is really quite a nice track as it twists and turns", and "a nice plodder".[10] Mike Soutar from Smash Hits called it a "latin-tinged sappy smoocher".[11]
A music video was produced to promote the single, featuring Estefan performing alone in a beach house. Sometimes she is seen standing by a large window, glancing out at the sea. Other times she sits by a table. In between there are also small clips of billowing water or a guitar that is being strummed. The video was later published on Estefan's official YouTube channel in March 2011. It has amassed more than 2,7 million views as of October 2021.[12]
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