Struggling Racing part company with Cuper
The 56-year-old Argentine joined a club in administrative turmoil during the summer and managed only one win in 13 matches.
"We would like to thank him for the way he has conducted himself on a personal and professional level in the agreement reached this afternoon when money wasn't the principal issue," Racing said in a statement.
"We are sorry for all the difficulties he has had to endure in managing his section against a background of great economic, institutional and social difficulties."
Cuper, who led Valencia to consecutive Champions League finals in 2000 and 2001, will be replaced by a temporary trio of Juan Jose Gonzalez, Fede Castanos and Pablo Pinillos until a new coach is found.
Racing accused the businessman who bought them in January, Indian Ahsan Ali Syed, of failing to honour his commitments.
They sought help from the regional government and the previous owners before going into administration in July with debts of over 33 million euros.