As an adolescent Mondragón entered the Military Academy of Chapultepec, where he specialised in artillery.

He modified the French 75mm howitzer, earning a name for himself among Porfirist military circles.

The artillery at the ports of Salina Cruz on the Pacific and Puerto México on the Gulf are due to his efforts.

At the side of General Bernardo Reyes and General Félix Díaz, Mondragón assisted in the start of the coup, known as the Ten Tragic Days, against democratically-elected President of Mexico Francisco I. Madero in February 1913.

He served in this position only a short time, resigning in June amid accusations from prominent Huertist politicians and public opinion blaming him for the advance of revolutionary forces opposed to Huerta's regime due to his incompetence and poor planning in the campaign against them.