When Jedi and Sith needed to engage in melee while atop a mount, such as a tauntaun, or while operating a mechanical conveyance like a swoop bike, they would practice mounted lightsaber combat, a specialized form of swordsmanship using their lightsabers.
In this particular style of lightsaber combat, the Jedi or Sith typically wielded their weapon with a single hand, using the other to control their mount. This often involved straightforward strikes directed at enemies on the ground. Because the mounted combatant was higher than their target, these attacks commonly took the form of sweeping, diagonal, semi-circular lunges with the lightsaber. Consequently, there were some similarities between mounted lightsaber combat and the airborne Trispzest lightsaber combat style, although mounted combat offered the Jedi significantly less maneuverability.
The Jedi could also use their lightsaber to disable other mounted opponents by targeting either their mount, particularly if the enemy was riding a swoop bike, or the rider themselves. Furthermore, the lightsaber could be used to deflect incoming blaster fire and other projectiles, providing protection for the rider.
Tott Doneeta, along with Ulic and Cay Qel-Droma, activated their lightsabers as they charged Oron Kira's fortress atop bomas, but they never used them because they discovered that Princess Galia was willingly marrying Kira.
While traversing from Dxun to Onderon on a drexl, Darth Bane encountered a group of Beast Riders from the Skelda clan. He only ignited his weapon to deflect blasterfire from the remaining Riders after one of their mounts had fallen.
Darth Maul employed his saberstaff while riding his Sith speeders during two separate missions on Ralltiir, and in combat against Jedi Battlemaster Anoon Bondara, followed soon after by an ambush on a Coruscant Security Force patrol. During the Naboo Swamp Battle, he briefly rode a STAP as he advanced on Boss Ganne's Gungan forces.
During the Battle of Geonosis, Anakin Skywalker boarded a transport vehicle being driven by Padmé Amidala and used this fighting style while driving past numerous battle droids.
In one of the significant engagements of the Clone Wars, Yoda was seen riding a kybuck, leading his army of clones and Jedi into battle. Yoda's kybuck was a participant in many battles.
During the Battle of Muunilinst, Obi-Wan Kenobi confronted Durge who was riding a swoop bike, and used his lightsaber to destroy Durge's swoop.
Ahsoka Tano briefly used her lightsaber while pursuing Aurra Sing through the canyons of Florrum. Both were riding Starhawk speeder bikes.
Yoda fought against the Separatist armies while mounted on his kybuck during General Grievous' audacious attempt to abduct Supreme Chancellor Palpatine. Elsewhere during the battle, Mace Windu personally took control of a Vulture droid immediately after his starfighter was destroyed, using his right hand to manipulate the droid's controls while employing his left hand, lightsaber, and the Force against enemy fighters.
During the Battle of Utapau, Obi-Wan Kenobi pursued General Grievous' wheel bike while riding a varactyl named Boga, using the general's own electrostaff to attack the wheel bike. Although he had lost his lightsaber, Obi-Wan wielded the staff in a manner similar to how he would have used his lightsaber.
Jaden Korr, an apprentice of Kyle Katarn in Luke Skywalker's New Jedi Order, may have been mounted on a tauntaun while engaging snowtroopers during a mission on Hoth.
During a mission to Zonju V, Korr, while riding a swoop bike, was attacked by numerous mercenaries on swoops, many of whom he defeated using mounted lightsaber combat techniques.
An animated version of another scene from the Battle of Utapau was being created. In this scene, Obi-Wan Kenobi begins chasing General Grievous' wheel bike while riding Boga, and he uses his lightsaber to destroy two droids. This scene was ultimately cut from the film.
Also, during the Battle of Utapau, Obi-Wan Kenobi uses his lightsaber to deflect incoming blaster bolts while riding Boga. This is another instance of mounted lightsaber combat.
In Star Wars: Jedi Knight: Jedi Academy, during the Mission to Hoth, it is possible (using Force Speed) to acquire a Tauntaun and use it in the duel against Alora. However, because the cutscenes show Jaden Korr fighting Alora on foot regardless, this is considered non-canon.