The album's title track, "Slow Me Down," was released as the album's lead-off single on September 23, 2013. It debuted at #57 on the U.S. BillboardCountry Airplay chart for the week of September 14, 2013, and ultimately reached a peak of number 17 in April 2014.
The second single was announced to be "Can't Stop Loving You" with a release date of July 21, 2014. For unknown reasons however, the release was pushed back to August 25, 2014 and then later cancelled completely with "Put My Heart Down" announced as the next single instead. "Put My Heart Down" was released on September 29, 2014. It debuted at number 60 on the U.S. BillboardCountry Airplay chart for the week of November 8, 2014, and ultimately reached a peak of number 57, only spending four weeks on the chart. Evans appeared on ABC's Nashville to perform a duet version of "Put My Heart Down" with Will Chase (who plays Luke Wheeler on the show) on October 29, 2014.
Slow Me Down garnered generally positive reception by music critics. At Metacritic, they assign a "weighted average" score to selected independent ratings and reviews, and based upon 5 reviews the album has a Metascore of an 87, which means the album received "universal acclaim". Erik Ernst of the Milwaukee Journal Sentinel gave a positive review, saying that the album "is a mostly joyful affair that finds the singer even more confident as she explores the many sides of love" on which "She's been there and has come out singing better than ever on the other side." At The Boston Globe, Sarah Rodman gave a positive review, stating that the release is better than her predecessor, and she says "the tracks that stand out have a fresh appeal." Jon Caramanica of The New York Times gave a positive review, and writes that Evans "robust and sweet voice" are what sets the album apart because "She sings with power, grace and dignity.". At USA Today, Brian Mansfield rated the album three out of four stars, stating that "In songs spanning soaring pop and stone country, Evans recounts all the ways to walk away, though she'd rather be convinced to stay", and the likes of "Gavin DeGraw, Vince Gill and Isaac Slade beckon her back."Stephen Thomas Erlewine of AllMusic rated the album four stars out of five, writing that "fans hoping that Evans will return to country music will be disappointed, but Slow Me Down is something that is rare in 2014: an unapologetic, big-scale adult pop album, constructed with grace and care." At The Oakland Press, Gary Graff rated the album three stars out of four, saying that Evans is "in fine voice and solid country-pop crossover form" on which "Evans isn’t about to be slowed down any time soon." Chuck Dauphin of Billboard rated the album a 91-out-of-100, stating that the album is spectacular making it hard to select a few highlight tracks. At Country Weekly, Tammy Ragusa graded the album an A, writing that "she has found what works best for her on the contemporary side and front-loads the project with those songs." At Got Country Online, Donna Block rated the album a perfect five stars, and according to her "Every single beat is felt, head to toe. It’s quite a feat to balance ever-changing feelings in a song, let alone throughout an album", and it shows just how Evans "maintains a vocal equilibrium from song to song" on the release. Dan MacIntosh of Roughstock rated the album three stars out of five, writing that Evans plays around with many styles on the album, but advises her "a beautiful, natural singing voice is a terrible thing to waste."
Slow Me Down debuted at number nine on the U.S. Billboard 200, and at number two on the U.S. BillboardTop Country Albums chart selling 27,000 copies in its first week of release. The album has sold 87,000 copies in the US as of August 2014.