Actually the stage company was Butterfield Stage Line. The Overland Mail was a contract with the Federal Government to carry the mail. There were many Overland Mail Contracts.
The Missouri Pacific Railroad carried the mail from St. Louis to Tipton, Missouri (1858) and Syracuse, Missouri (1859-1861) where the stage line warehouses were located. The route (required by federal contract) went south to Arkansas and then west through Texas, up through New Mexico, Arizona and north to San Francisco.
The stage line used mules through Texas, because Indians didn't like them and would not attack the stages if no horses were used.
With the outbreak of the Civil War, Union troops came into Syracuse, Missouri and burnt the railroad station and all the warehouse in town. Syracuse was a city of 5,000 in those days, it is a town of 250 today. Syracuse being of Southern sympathies the Union troops also pulled Southern residents into the streets and executed them.
This caused Mr. Butterfield to move his stage routes further north, and the Federal Government released him from that requirement in the original contract.
Suggest you visit Missouri Historical Markers (link above) and read the many markers there. Almost all of the relay stations in Missouri have been found and marked.