Yamada was born in Gunma Prefecture on November 28, 1984. She enjoyed drawing as a child and would copy images from the Patlabor and Dragonball anime series. She joined the volleyball club in primary school and the tennis and photography clubs in high school. At the Kyoto University of Art and Design, she studied oil painting and was a member of the special effects club.
After working as an episode Director of Clannad, she was asked to make her chief directorial debut with K-On!, an adaptation of a slice-of-life manga. The series was very successful, spurring a second season and a film. In 2013, she directed Tamako Market, and followed it with the film Tamako Love Story in 2014. For Tamako Love Story, she was awarded the New Face Award at the Japan Media Arts Festival. She storyboarded the entire film herself, and also wrote the lyrics for the opening theme song, Everybody Loves Somebody. Yamada's next project was the feature film A Silent Voice, an adaptation of the manga of the same name, that reflected on elements of bullying and physical impairment in Japan. The film opened at #2 in the Japanese Box Office and grossed a total of ¥2.3 billion, the 19th highest-grossing film in Japan in 2016. The film also received multiple award nominations, including Best Animation Film in the Mainichi Film Awards and the Excellent Animation of the Year in the Japan Academy Prize.