Asplund grew up in the suburbs of Stockholm, Sweden. She has a Polish mother, Swedish father, and older sister. When she was seven-years-old, her parents got divorced and she mainly lived with her mother and stepfamily from then on.
She started acting at the local theater close to her home at the age of six. Asplund attended Södra Latins Gymnasium (Southern Latin secondary school) from 2007 - 2010 in Stockholm, Sweden. She studied acting. She also took lessons at Calle Flygares Teaterskola in 2009.
She is mostly known for playing Pernilla Blomkvist in The Girl with the Dragon Tattoo (2011). She plays one of the lead roles in the film adaptation of the best selling Swedish novel The Circle (2015).