Anderson started out as a mud bogger with his original Grave Digger in 1981. This truck was a 1952 Ford pickup truck. It was later converted to a silver and blue 1951 Ford Panel Truck. Anderson gained a reputation for an all-or-nothing driving style and quickly became popular at local events. At one show, a scheduled monster truck failed to show up and Anderson, who already had large tractor tires on the truck, offered to crush cars in the absence of the full-size monster. The promoter accepted and Grave Digger was an instant success as a car crusher and led Anderson to leave mud bogging and pursue monster trucks instead.

In 1986 Grave Digger underwent a transformation to complete monster truck and first received its famous black graveyard paint scheme. In 1987 and 1988 Anderson drove the truck primarily at TNT Motorsports races and became a crowd favorite for driving hard despite lacking major funding that better-known teams, like Bigfoot, had. In 1987 Anderson beat Bigfoot in St. Paul, Minnesota, on a show taped for ESPN. It was his first major victory.

With a points championship now in place, Anderson moved to Grave Digger 2 in 1989, with a new 1950 Chevy panel van body. It was during this time that the reputation for wild passes was developed, and Anderson became a superstar in earnest. TNT recognised his rising popularity and began promoting Grave Digger heavily, especially for races on the Tuff Trax syndicated television series and ESPN's Powertrax. This was helped by Bigfoot running a limited schedule in the 1989 championship, leaving Grave Digger as the most popular truck on the tour. He was currently sixth in the standings in the 1990 TNT series when he decided to build Grave Digger 3 due to a wreck.

When TNT became a part of the USHRA in 1991, Anderson began running on the USHRA tour and debuted his first four-link truck, Grave Digger 3. Throughout the 1990s, the popularity of the truck grew and forced Anderson to hire other drivers to run other Grave Digger trucks. However, Anderson was still the driver most connected to the truck, and his appearances at shows promoted him as much as the truck. It is also during this time period in which his freestyle reputation came into being. Even in this period of exhibition freestyles he made it a point to drive harder than other competitors, and it led to his runs being the most anticipated at shows.

In late 1998, Anderson sold the Grave Digger team to Clear Channel. Despite no longer owning the truck, he continues to be the primary driver and the most heavily promoted. The sale of the truck led to controversy and accusations of rigged races as he is driving for the same company that runs the events he competes in. There has been little solid evidence of this occurring, however, and Anderson insists that he wants to win fairly and has even publicly called out freestyle judges when he felt runs were scored too high. In 1999 he won his first championship in the USHRA series. In 2001, Dennis drove Mr. Destruction into a wall of cars as a special stunt for the Louisiana Superdome show. Anderson won the inaugural Monster Jam World Finals freestyle championship in 2000, and scored a popular racing championship win at the 2004 World Finals.

Anderson currently drives Grave Digger 20. The truck, which is somewhat similar to Grave Digger 19, debuted in Minneapolis in December 2005. In Grave Digger 20, he scored yet another racing championship at the 2006 World Finals, at the same event he debuted Grave Digger 20 his son Adam Anderson made his pro debut in the Taz truck.