Spurs lost 3-0 to Manchester United at the weekend, a result which left the club sitting 8th in the table after ten games.
Espírito Santo was appointed as the replacement for Jose Mourinho in June on a two-year deal and took former Hearts manager Cathro with him as part of his coaching staff following their success at Wolves.
However, back to back league defeats increased fan disgruntlement on the back of losing the North London derby to rivals Arsenal at the end of September.
Fabio Paratici, the club's managing director, said: "I know how much Nuno and his coaching staff wanted to succeed and I regret that we have had to take this decision.
“Nuno is a true gentleman and will always be welcome here. We should like to thank him and his coaching staff and wish them well for the future.”