The mission was launched from Kennedy Space Center in Florida on July 13, 1995, only six days after the landing of sister ship Atlantis, marking the fastest turnaround between flights in the history of the program.

Engine number 2036 featured the new high-pressure liquid oxygen turbopump, a two-duct powerhead, baffleless main injector, single-coil heat exchanger and start sequence modifications.

The primary mission was the launch and deployment of the 7th Tracking and Data Relay Satellite (TDRS-G) by means of the two-stage Inertial Upper Stage (IUS) solid rocket.

[3] At about 3:55 p.m., the IUS fired the first of two burns that would put TDRS-G into its proper, 22,000-mile-high geostationary orbit above the central Pacific Ocean at 178 degrees West longitude.

The on-orbit TDRS network was rearranged and included two fully operational spacecraft occupying the TDRS East and West slots, one on-orbit fully functional spare, TDRS-1, which was nearly depleted having exceeded its planned lifetime, and the partially operational TDRS-3 spacecraft dedicated to supporting the Compton Gamma Ray Observatory and providing coverage an area that can't be seen by the other satellites known as the Zone of Exclusion.

Secondary objectives of the mission were to fulfill the requirements of the Physiological and Anatomical Rodent Experiment / National Institutes of Health-Rodents (PARE/NIH-R); Bioreactor Demonstration System (BDS), Commercial Protein Crystal Growth (CPCG); Space Tissue Loss/National Institutes of Health-Cells (STL/NIH-C); Biological Research in Canisters (BRIC); Shuttle Amateur Radio Experiment-II (SAREX-II), Visual Function Tester-4 (VFT-4); Hand-Held, Earth Oriented, Real-Time, Cooperative, User-Friendly, Location-Targeting and Environmental System (HERCULES); Microcapsules in Space-B (MIS-B); Windows Experiment (WINDEX); Radiation Monitoring Equipment-III (RME-III); and the Military Applications of Ship Tracks (MAST).

The BDS was composed of a device developed at the Johnson Space Center that used a rotating cylinder to suspend cells and tissues in a growth medium, simulating some aspects of microgravity.

Flight Director Rich Jackson directed the five STS-70 astronauts to remain aloft for another day after poor visibility prevented Discovery's homecoming on the two consecutive landing opportunities.

Nose gear touchdown occurred at 8:02:11 am EDT (Mission Elapsed Time of 8 days 22 hours 20 minutes and 16 seconds) with wheels stop at 8:02:57 am (MET of 8 d 22 h 21 min 2 s).