Blackwood was born in San Antonio, Texas and graduated from Churchill High School.

He was a Dolphins nominee for the NFL Man of the Year and for the Ed Block Award for inspiration, sportsmanship and courage.

[3] His brother Lyle Blackwood also played in the NFL, and they were teammates from 1981 through 1986 with the Miami Dolphins.

On a Monday night game against Buffalo in 1981, Glenn at strong safety and Lyle at free safety ganged up to put some heavy hits on the Bills’ players, prompting a Miami sportswriter to dub them "The Bruise Brothers."

His son Glenn Jacob "Jake" Blackwood played football at Georgia Tech.