Crutchfield was born on June 21, 1835, on the Spotsylvania County plantation of his parents, Oscar Minor Crutchfield, Speaker of the House of Delegates from 1852 to 1861, and Susan Elizabeth M. Gatewood Crutchfield. He matriculated at the Virginia Military Institute in 1851 but was sent home after only a few months for disciplinary reasons. He returned to the institute the next year and graduated first in his class in 1855. For the next six years Crutchfield served on the VMI faculty, first as an assistant and after 1858 as a full professor of mathematics, one highly regarded by his students. While living in Lexington, Crutchfield was confirmed in the Episcopal Church and joined the Franklin Society and Library Company of Lexington, a lending library and debating club.
When the Civil War began in the spring of 1861, Crutchfield remained inand served for about three months as temporary superintendent of VMI. In this capacity he supervised the shipment to of 10,000 muskets from the state arsenal located at the school and served as a drillmaster for new units raised in the region. On May 1, 1861, Crutchfield was commissioned a major in Confederate service. Assigned on July 7 to the 9th Virginia Volunteer Regiment, he reported for duty at Craney Island later that month. On October 1, Crutchfield became a major in the 58th Virginia Infantry Regiment, but illness prevented his participation in the autumn campaign in western Virginia. Elected lieutenant colonel of the 58th Virginia early in 1862, he was dropped from the roster when the regiment reorganized on May 1. Two days later he was elected colonel of the 16th Virginia Infantry Regiment but for health reasons declined to serve.
On May 17, 1862, his friend and former VMI colleague Stonewall Jackson secured for him a commission as colonel and appointed Crutchfield his chief of artillery. Crutchfield saw his first action at Front Royal on May 23, 1862, in Jackson’s. On the morning of June 8, Union cavalry surprised Jackson and his staff at . Briefly captured while attempting to leave the village, Crutchfield escaped during a Confederate counterattack and rejoined Jackson’s army. That summer he participated in the around Richmond, , , and the capture of during the . In November 1862 Jackson’s command became the Second Corps of the Army of Northern Virginia, and Crutchfield directed its artillery. At he commanded the guns on the southern part of the battlefield.
In mid-April 1863 Jackson recommended Crutchfield for promotion to brigadier general, but the request was passed over and Crutchfield remained a colonel. At Chancellorsville he was severely wounded by a shell fragment that shattered a bone in his right leg below the knee. Crutchfield left the battlefield in the same ambulance that carried the mortally wounded Jackson. The leg wound removed Crutchfield from active service for the remainder of 1863. In the autumn of that year the VMI board of visitors elected Crutchfield to fill Jackson’s former chair as professor of natural philosophy. He declined the offer of a permanent position but taught on a temporary basis while he recuperated.
On March 16, 1864, having sufficiently recovered, Crutchfield was assigned to duty in the Confederate Ordnance Bureau as inspector of seacoast batteries. He petitioned for field service and on January 18, 1865, returned to active duty with the Army of Northern Virginia as commander of a heavy-artillery brigade stationed at Chaffin’s Bluff in the Richmond defenses. During the Appomattox Campaign, Crutchfield’s brigade was attached to George Washington Custis Lee‘s division. On April 6, 1865, at Sailor’s Creek, Crutchfield was leading a charge when an artillery shell decapitated him. His body was left on the field by the retreating Confederate forces and probably was buried there by local citizens.