He played college football for the West Virginia Mountaineers and was selected by the Oakland Raiders in the first round of the 2016 NFL draft.

[7] Coming out of West Virginia, Joseph was projected by the majority of NFL draft experts and scouts to be a second or third round pick.

He received an invitation to the NFL combine, but was unable to perform any physical drills due to a knee injury he suffered in October.

On April 4, 2016, he was among 22 prospects who performed at West Virginia's pro day, that included Wendell Smallwood, K. J. Dillon, Nick Kwiatkoski, and Daryl Worley.

[13][14] Joseph competed with veterans T. J. Carrie and Nate Allen throughout training camp for the vacant starting strong safety role after the departure of Larry Asante.

[15] Head coach Jack Del Rio named Joseph the backup strong safety to Nate Allen to begin the 2016 season.

On September 25, 2016, Joseph made his first career start and recorded a season-high ten combined tackles in the Raiders' 17–10 victory at the Tennessee Titans.

On October 9, 2016, he collected six combined tackles, defended a pass, and made his first career interception off of Philip Rivers during a 34–31 victory over the San Diego Chargers.

The following week, Joseph recorded five combined tackles, his first career sack, and forced a fumble by New York Jets quarterback Josh McCown, that he would recover to set up the Raiders' offense on an eventual touchdown scoring drive.

[23] On October 19, 2017, Joseph recorded four combined tackles and a pass deflection, but exited the Raiders' 31–30 victory at the Kansas City Chiefs in the fourth quarter after sustaining an injury.

[25] On December 31, 2017, the Oakland Raiders fired head coach Jack Del Rio and finished third in the AFC West with a 6–10 record.

Starting from week 11, Joseph's play improved and he finished the season as the Raiders' highest graded defender according to Pro Football Focus.

In week 10 against the Los Angeles Chargers on Thursday Night Football, Joseph recorded an interception off Philip Rivers late in the fourth quarter which sealed a 26–24 win.

[39] In the divisional round of the playoffs against the Chiefs, Joseph intercepted a pass thrown by Chad Henne in the endzone for a touchback during the 22–17 loss.