Though July 1 marks the start of the Gettysburg tussle, Vicksburg in July 1 of 1863 was on it's last leg as well.
The big event was a second mine detonated in the outer lines on July 1:
From Wiki
Late in the siege, Union troops tunneled under the 3rd Louisiana Redan and packed the mine with 2,200 pounds of gunpowder. The explosion blew apart the Confederate lines on June 25, while an infantry attack made by troops from Logan's XVII Corps division, followed the blast. The 45th Illinois Regiment (known as the "Lead Mine Regiment"), under Col. Jasper A. Maltby, charged into the 40-foot (12 m) diameter, 12-foot (3.7 m) deep crater with ease, but were stopped by recovering Confederate infantry. The Union soldiers became pinned down while the defenders also rolled artillery shells with short fuses into the pit with deadly results. Union engineers worked to set up a casemate in the crater in order to extricate the infantry, and soon the soldiers fell back to a new defensive line. From the crater left by the explosion on June 25, Union miners worked to dig a new mine to the south. On July 1, this mine was detonated but no infantry attack followed. Pioneers worked throughout July 2 and July 3 to widen the initial crater large enough for an infantry column of four to pass through for future anticipated assaults. However, events the following day negated the need for any further assaults.
Nice website for quick overview, plus a plug for HPS Vicksburg
http://americancivilwar.com/vicks.html
Col. Elkin
AotT