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Semplici had been at the helm since December 2014, leading the club from Serie C to the top flight for the first time in 49 years from the 2017-2018 campaign.
The 52-year-old's dismissal follows a poor run including Sunday's 2-1 defeat at home against Sassuolo.
SPAL have won just four games this season against Lazio, Torino, Parma and Atalanta, and are bottom of the table with 15 points from 23 games.
Former Italy midfielder Di Biagio spent six years as coach of Italy's U21 side and was also caretaker coach of the senior national team for three months in 2018.
He eventually made way for Roberto Mancini after the Azzurri's failure to qualify for the 2018 World Cup.
The 48-year-old ex-Roma and Inter Milan player has signed a contract until June 30 next year, with his first game at fellow strugglers Lecce on Saturday.
