The Battle of Stone Mill is a major engagement in the War of the Five Kings. It is recounted by Edmure Tully in his report to King in the North Robb Stark in "Walk of Punishment", the third episode of Season 3. Chronologically, the timing of the battle is not given but seems to be after the Battle of the Blackwater, which happened in the ninth episode of Season 2.
Having decided to give up his stronghold at Harrenhal, Lord Tywin Lannister and the bulk of the Lannister army marched south-east to King's Landing to engage the forces of Stannis Baratheon. Tywin left Ser Gregor Clegane, the Mountain, in command of the garrison at Harrenhal, instructing him to ravage the countryside.
The Stark army under King Robb Stark abandoned its invasion of the Westerlands - now fruitless since they lacked the strength to attack Casterly Rock - and marched east to besiege Harrenhal and flush out the Mountain. However, upon their arrival they discovered that the Mountain had already slaughtered the prisoners at Harrenhal and fled.
Tactically, the battle was an amazing success, inflicting disproportionate losses on the Lannisters and forcing Gregor Clegane to retreat from the Red Fork of the Trident. They fell back on Casterly Rock. This removed them from being in immediate striking distance of Riverrun itself. Tywin's young nephews, Willem and Martyn Lannister, are taken hostage in the battle.
Strategically, the battle was a significant blunder. Robb Stark's plan was to lure Gregor Clegane's forces further west into the Riverlands where they could be surrounded and destroyed. Edmure's attack instead allowed Clegane to escape.
In the books
In the Song of Ice and Fire novels, the battle is similar but takes on a considerably greater strategic significance. In the novels the main Lannister army under Tywin was lured by Robb from Harrenhal and marched west, Tywin facing unrest from his bannermen as Robb's forces ravaged their homeland. Tywin's main army attempted to cross the Red Fork of the Trident south of Riverrun, only to face significant Riverlands opposition led by Edmure Tully, who seized the opportunity to prove himself a battle commander the equal of his nephew.
The battle was fought over an extremely wide front, encompassing fords to the south and north of Riverrun, and featured the entire main Lannister army attempting to cross the river. Edmure's forces were fewer in number but held the strategic high ground on each side of the fords, and were able to subject the Lannister forces to withering arrow fire as they attempted to cross. Ser Jason Mallister commanded the defense of four fords to the south of Riverrun, and Karyl Vance commanded the defense of fords to the north, while Edmure Tully commanded the defense of the fords closest to Riverrun itself. The fiercest assault came at Stone Mill in the center, where the forces commanded by Ser Gregor Clegane himself managed to gain a foothold on the west bank of the river despite suffering terrible losses, but were then driven back when Edmure hit them with his reserves.
The entire campaign was led by Tywin, whilst Gregor Clegane personally commanded the main thrust at Stone Mill. Whilst the battle was raging, Tywin received word that Stannis Baratheon was about to attack King's Landing. He withdrew from the engagement, turned his army south and marched to the headwaters of the Blackwater Rush. They built barges and skiffs and were able to rapidly head downriver, meeting the army of House Tyrell along the way. This allowed the combined Lannister and Tyrell armies to then attack Stannis's flank at the Battle of the Blackwater, routing him.
Robb later chastises Edmure for his blunder, saying that the northmen had identified a valley in the western mountains where they planned to lure Tywin Lannister into a trap and destroy his main army. By preventing his crossing, Edmure won a strategically meaningless short-term victory at the cost of a possible long-term victory for the entire campaign. Edmure angrily pointed out that the blunder was due to Robb not trusting him with his plans.
In the TV series the timing and nature of the battle is changed. The entire battle now takes place at the Stone Mill and seems to be much smaller in scale, with Gregor's forces consisting almost solely of the garrison Tywin left him at Harrenhal. Rather than being forced to retreat eastwards to King's Landing, Gregor's forces were instead forced to retreat westwards to Casterly Rock. The overall strategic significance of the battle was also downplayed: in the TV series it only meant that the Mountain would survive to cause further problems later on.
One minor change is about Martyn and Willem Lannister: none of them was taken captive at the Battle of Stone Mill, and not by the Tullys. Willem and his cousin Tion Frey were captured by the Starks at the Battle of the Whispering Wood, while Martyn was captured at the Battle of Oxcross.