Mims played college football at New Mexico State, and joined the Calgary Stampeders in 1971. In his rookie season, Mims played all 16 games and along with Hugh McKinnis who was playing his second season with Calgary after an outstanding rookier season, gave the Stampeders an excellent 1-2 running punch. McKinnis finished fourth in rushing in the West and Mims finished fifth with 834 yards on 146 carries and a very good 5.7 yards per carry average. Mims also caught 37 passes for 454 yards, an average of 12.3 yards per catch which is very good for a running back. In 1973, Mims missed four games due to injuries and that accounted for a slight drop in his rushing yards to 728, good enough for fourth in the West. Mims only played two games in 1973, his third and last with the Stampeders. After leaving Calgary, Mims played with the Detroit Wheels of the WFL in 1974.
| Year | Team | GP | PA | PC | % | Yds | TD | Int | Sacked | Yds | TC | Yds | Avg | TD | Rec | Yds | Avg | TD | Long | PTS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1971 | CAL | 16 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 9 | 146 | 834 | 5.7 | 2 | 37 | 454 | 12.3 | 3 | 47 | 30 |
| 1972 | CAL | 12 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 132 | 728 | 5.5 | 6 | 16 | 188 | 11.8 | 1 | 42 | 42 |
| 1973 | CAL | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 19 | 54 | 2.8 | 0 | 9 | 110 | 12.2 | 1 | 21 | 6 |
| Year | Team | KOR | Yds | Avg | TD | Long |
|---|---|---|---|---|---|---|
| 1971 | CAL | 8 | 215 | 26.9 | 0 | 35 |
| 1972 | CAL | 12 | 304 | 25.3 | 0 | 31 |
| 1973 | CAL | 0 | 0 | 0 | 0 | 0 |
| Year | Team | F | FL |
|---|---|---|---|
| 1971 | CAL | 8 | 6 |
| 1972 | CAL | 5 | 5 |
| 1973 | CAL | 0 | 0 |