A native of southwest Virginia, Joseph was born and raised in Giles County and is an alumnus of Giles County Public Schools. He is a graduate of Radford University earning both a Bachelors of Science and a Masters of Arts in Criminal Justice in 4 years. He is a 2011 graduate of The Sorensen Institute for Political Leadership at the University of Virginia and a 2013 graduate of The Buckley School for Public Speaking. Joseph is a proud southwest Virginian never shying away from his nickname as the "Scholar from the Hollar."

Joseph traces his family's roots to the mid-1600s in Germany. In 1733, his seventh great-grandfather, Hans Casper Yost, boarded a ship bound for America landing at the port of Philadelphia in August. After settling near present-day Lancaster, Pennsylvania, his family moved to George Town, MD (present day Georgetown, Washington, DC). There, his sixth great-grandfather, Henry Yost, owned and operated a gunsmith's shop and produced arms for the Continental Army. He also signed the Oath of Fidelity for the State of Maryland, was a member of the Committee of Observation and served as a Lieutenant in the Maryland militia. Since that time, members of Joseph's family have served in the War of 1812, the Civil War, World War I, World War II and the Korean War.

He currently volunteers as a historical interpreter for Historic Smithfield Plantation and serves as a Board Member on the Smithfield-Preston Foundation. Joseph is a member of the Sons of the American Revolution: The Fincastle Resolutions Chapter, the New River Valley Re-entry Council, the New River Valley Smart Beginnings Leadership Council, the Giles County Extension Leadership Council, and founding member of the Virginia Tech STEM Advisory Board. He is also a member of the Giles County Chamber of Commerce, the Montgomery County Chamber of Commerce and is an A.F. & A.M. with Castle Rock Lodge No. 334.

Joseph is a dedicated Republican and is a member of the Giles County Republican Party. Previously, he was a member of the Montgomery County Republican Party from 2009-13. During that time, he served as Secretary and in other leadership roles such as Parliamentarian at meetings and Precinct Captain. In 2011, he helped reinvigorate Roanoke/New River Valley Young Republicans and served as Chairman from 2011-2012 before being elected to the House of Delegates.

At 28, he is the youngest member of the General Assembly and was first elected in November, 2011. He currently serves on four committees: Education; General Laws; Health, Welfare, & Institutions; and Privileges & Elections. He also serves as Vice-Chair of the Privileges and Elections subcommittee on Campaign Finance.

Joseph also serves on a variety of authorities, boards and commissions including the Substance Abuse Services Council, the Board of Trustees for the Center for Rural Virginia, the Dr. Martin Luther King Jr. Memorial Commission, the Board of Trustees for the Southwest Virginia Higher Education Center, the Board of Trustees for the Southwest Virginia Cultural Heritage Foundation, the Southwest Virginia Health Facilities Authority, the Western Virginia Public Education Consortium, and as Chair of the Virginia Health Workforce Development Authority.

He was previously a member of the Governor's Task Force for School and Campus Safety and the Governor's Task Force on Mental Health Services and Crisis Response. He is currently a member of the Joint Subcommittee to Study Mental Health Services in the Twenty-First Century and Chairs the Special Populations Work group which is tasked at looking at the mental health system as it related to children, veterans, co-occuring disorders, traumatic brain injuries and intellectual and developmental disabilities.

During his time in the House, Joseph has become a leader on issues relating to education and mental health. In 2012, he was named the “Legislative Rookie of the Year” by the Virginia Education Association and in 2013, he was named the “Legislative Champion of the Year” by the Virginia Education Association, “Legislator of the Year” by the Psychiatric Society of Virginia, "Legislator of the Year" by NAMI Roanoke Valley and "Legislator of the Year" by the Virginia Counselors Association. He was also named a "Distinguished Advocate for Virginia Business" by the Virginia Chamber of Commerce in 2012 and 2013.

In 2014, he was named "Legislative Champion of the Year" by the Virginia Education Association, received the "Rising Star Award" from the Virginia Association for Early Childhood Education and was named a "Champion of Free Enterprise" by the Virginia Chamber of Commerce. He was also named "Legislator of the Year" by the Virginia Treasurer's Association. In 2015, he was given the "Solid as a Rock" Award by the Virginia Education Association.

Joseph has spent his entire life within the boundaries of the 12th District. In June of 2010, he married Lisa Robinson Yost. They reside in Pearisburg. In addition to his duties as a Delegate, he is also the Executive Director of the Giles County Historical Society.