The following information came from Wikipedia:

A native of Virginia, Spencer moved to Kentucky with his parents. He married Elizabeth Polk, daughter of Capt. Charles Polk, in Bardstown, Nelson County, Kentucky on January 18, 1793. Spencer and his wife moved to Vincennes, Indiana. In 1809 Spencer was appointed by Governor William Henry Harrison as the first sheriff of Harrison County, Indiana. He moved his family to Corydon and served in that office until his death.

Spencer and his wife ran "The Green Leaf Tavern," in their large log home on Oak Street. Governor William Henry Harrison and Lieutenant Governor Ratliff Boon stayed there when they came on official business, as did delegates to the 1816 Indiana Constitution Convention.

When tensions between the settlers and the Native Americans became serious, Spier Spencer organized a Harrison County mounted militia company known as the "Yellow Jackets" for their uniforms. They would engage in a campaign against the Shawnee Indians under Governor Harrison. Spencer was seriously wounded in the head and thighs during the November 7, 1811 Battle of Tippecanoe. As he was being carried to safety, he was struck and killed by another musket ball.

Spencer's death was described by General Harrison in his report to the secretary of war on the 18th of November:

"...Spencer was wounded in the head. He exhorted his men to fight valiantly. He was shot through both thighs and fell; still continuing to encourage them, he was raised up, and received a ball through his body, which put an immediate end to his existence..."

Spencer and his men were praised for their bravery by General Harrison.

In 1818, Spencer County, Indiana, was named for him, as was in 1820 the town of Spencer, Indiana in Owen County. Spencer County, Kentucky was created and named for him in 1824.

The following is from the book "Polk Family and Kinsmen" written by W. H. Polk, November 28, 1912 concerning the dedication of Spencer County Kentucky:

This county was named in honor of Capt. Spier Spencer, a young man of ardent patriotism and undaunted courage, who fell at the head of his company in the battle of Tippecanoe. He commanded a fine rifle company in that severe engagement, and occupied a most exposed position. In the midst of the action, he was wounded on the head, but continued at his post, and he exhorted his men to fight on. Shortly after he received a second ball, which passed through both thighs and he fell, but still resolute and unyielding, he refused to be carried from the battlefield, and urged his men to stand to their duty. By the assistance of one of his men he was raised to a sitting posture, when he received a third ball through his body, which instantly killed him. Both of his Lieutenants, Messrs. McMahn and Berry, were both killed. Capt. Spencer was a warm friend and bosom companion of the gifted and gallant Daviess, who perished with him in the battle.

It is interesting that Spencer County was once part of Warrick County which took in all of present day Perry, Posey, Spencer, Vanderburgh and Warrick counties. Warrick County was organized by the legislature in 1813 and named for Captain Jacob Warrick, who was also killed in the Battle of Tippecanoe in 1811.