Mower was born in Woodstock, Vermont. He volunteered as a private in the Mexican–American War. In 1855 he entered the U.S. army as a 2nd Lieutenant in the 1st U.S. Infantry. As part of the 1st US Infantry, Mower saw action in the Battle of Wilson's Creek in August 1861. Still with the regiment during the Battle of Island No. 10, Major-General John Pope selected Mower to construct a siege battery in front of New Madrid, leading to the capture of that river port early in the campaign. He later became colonel of the 11th Missouri Infantry Regiment and fought at the Siege of Corinth. He assumed command of the 2nd Brigade of the 2nd Division in the Army of the Mississippi and led it into action at the Battle of Corinth. He was wounded in the neck and taken prisoner by Confederate forces but he was recovered by Union soldiers the same day.