On May 1, 1863, Grant's superiority of forces (more than 2:1) over Gen Bowen at Grand Gulf defeated the Confederates and now threatened Jackson, MS and also Vicksburg and Port Hudson. If Vicksburg could be defeated, it would cut the South in two, removing its food sources in Texas, Louisiana and Missouri, blocking the only open shipping route from Europe, Vera Cruz, Mexico by way of Texas and river freight to Vicksburg. Vicksburg was the only remaining railhead for transshipment throughout the South. With New Orleans and Memphis already lost, the loss of Vicksburg would mean slow strangulation of the South and almost certain eventual defeat. Gen Pemberton set up a defense line along the Big Black River to protect Vicksburg from siege. Pemberton had about 23,000 troops, but Grant had 45,000. Grant decided to sever the rail connection between Vicksburg and Jackson near the Big Black River railroad crossing. By May 14th, Sherman captured Jackson and laid waste to the city and surrounding areas.
Gen Joseph E. Johnston (commander of the Trans-Mississippi from TN to the Gulf) was forced to move from TN with with 6000 troops to try to stop Sherman's 25000. Pemberton tried to link up with Johnston near Jackson. Pemberton was forced to take 17,500 troops, leaving 6000 to defend Vicksburg and the principal crossings of the Big Black. May 15, 1863, Johnston was a day's march N of Jackson. Pemberton was defeated at Champion Hill, 12 miles short of his goal.
Pemberton's army was forced back to a position just E of the Big Black River Bridge, Sunday, May 17, 1863. Yankee forces attacked along the river at the bridge. The confederates fell back. Sensing a loss of the bridge, which would mean a full attack on Vicksburg before the army could get back to their defensive positions, Pemberton ordered the bridge burned with defenders still on the wrong side of the burning bridge. 1751 were captured. Grant quickly had the bridge rebuilt, but enough defenders were able to get back to Vicksburg. Grant laid siege to the city and forced surrender or starvation.
Vicksburg surrendered on July 4th. An irony is that the forces at Vicksburg were freed during July (It would have taken too many Union troops to get them to prison camps.) Whereas those who had been captured at Champion's Hill and Big Black River Bridge were not repatriated until December 25th.