How did Antonio Lopez de Santa Anna help to contribute to the causes of the Mexican Revolution of the 1910s?
Santa Anna did not, of course, have anything personally to do with the revolution as he died in 1876. However, you can argue that his actions helped to set the scene for that revolution.
From the time that Mexico became independent to the time that the Emperor Maximilian was defeated and killed (1867), Santa Anna was involved in a constant struggle for power between liberals and conservatives in Mexico. This constant struggle weakened the country badly and helped to allow such things as the loss of half the country's territory to the United States in the 1840s.
Because of all this chaos and the economic and political weakness that came with it, Mexicans wanted stability and progress. This led to the rise of Porfirio Diaz, who essentially became the dicatator of Mexico. Diaz's long reign gave rise to the Revolution.
So, Santa Anna and his constant attempts to take power helped to weaken Mexico. This helped make the Porfiriato possible. The Porfiriato led to a backlash which was the Revolution. In this way, Santa Anna helped create the conditions that led to the Revolution.