Mihok was born in New York City, New York, the son of actors Andrea Mihok (née Cloak) and Raymond Thorne (né Mihok). He has two older sisters: Gwen Mihok, an actress, and Cecily Trenka, a science teacher. He is of part Czech descent.
He grew up in Greenwich Village and lived in the artist community Westbeth on Bank Street. Mihok went to PS 3, a public elementary school in Manhattan, currently named the John Melser Charrette School. He attended the Center School (MS 243) for middle school. While attending Bronx High School of Science, where he played baseball as a middle infielder, Mihok joined CityKids Repertory, and appeared in on the short-lived TV show, CityKids. Mihok also attended the Professional Children's School in Manhattan with best friend, actor Donald Faison.
He attended Fordham University for some pre-college, but started working around the age of 18 so never completed his degree.
Mihok has been featured in roles in films such as The Day After Tomorrow, The Perfect Storm, The Thin Red Line, Lifted, Romeo + Juliet, I Am Legend, and Silver Linings Playbook. He has had starring roles in independent features such as Telling You and Loveless in Los Angeles.
Mihok studied Shakespeare to prepare for Romeo + Juliet, and had five extensive audition sessions with director Baz Luhrmann before landing the role of Benvolio.
For Terrence Malick's The Thin Red Line, Mihok said he spent an intensive six months working on the film, with the amount of footage constituting a full starring part, but during editing was reduced to an ensemble role.
He played Detective Martin Soap in the film Punisher: War Zone, which was released in December 2008.
Mihok currently co-stars as Brendan "Bunchy" Donovan in the Showtime drama Ray Donovan. For the show the cast works out at the Santa Monica, California boxing gym Wild Card West with boxer Rob Garcia. In 2014 he portrayed Whelan, in the Horror-thriller film Before I Wake and co-starred in the Mike Flanagan directed film Annabeth Gish, Thomas Jane and Kate Bosworth.
Mihok studied dance. He can be seen dancing opposite then-girlfriend Alanis Morissette in her music video "So Pure".
Mihok is a photographer as well. His photography of Morissette is used on the back cover of her "Thank U" single and is credited for Supposed Former Infatuation Junkie.
Mihok appeared on Sicilian-Puerto Rican New York-based rapper Sabac Red's record Sabacolypse: A Change Gon' Come, on the track "I Have A Dream." The lyrics refer to tics.
Mihok directed a short film called Abby in 2011. The film stars his sister, Gwen.
Mihok portrayed the character "Gage" in the 2013 Payday 2 web series.
Mihok was named after writer Dashiell Hammett, the author of The Thin Man, The Glass Key and The Maltese Falcon. His last name is usually mispronounced "me-Hawk," but he says the Czech surname is pronounced "my"-Hawk.
Mihok was diagnosed with Tourette syndrome at age six, and is the spokesperson for the nonprofit Jaylens Challenge, as well as an active supporter of the Tourette Syndrome Association.
Mihok said that one reason he became an actor was probably because he was experienced so well in hiding his Tourette's, that he was acting all the time. He said the focus required of acting allows him to mask many of his tics. Mihok says the biggest misconception about Tourette's Syndrome is about vocal tics, called coprolalia. Not everyone with Tourette's does that: "Tics tend to wax and wane, not everybody's screaming obscenities all the time." Mihok said he took medication during high school for the Tourette's.
In 1997, Mihok met Alanis Morissette through friend Leonardo DiCaprio during a trip to Cuba. The lyrics to the songs "So Pure" from Supposed Former Infatuation Junkie and "That Particular Time" from Under Rug Swept are about him.
In 2009, Mihok married singer Valeria Mason.