Gur was born in Jerusalem and later joined the Haganah (the underground armed group of the Jews in the British Mandate of Palestine). He continued serving in a military capacity with the founding of the Israel Defense Forces (IDF) during the Israeli War of Independence in 1948.
After he returned he was appointed as the commander of the Golani Brigade (1961-1963) and commanded the counter-terror raid in Nukiev. He brought over the traditions and attitude of the Paratroopers, raised morale, and helped instill an espirit de corps in Golani for which the brigade is still famous. In 1965 he was appointed as the head of the operations branch in the general staff of the IDF. He later also served as a commander of the IDF commanders' school.
In 1966 Gur was appointed as the commander of the 55th (Reserve) Paratroopers Brigade, which he led during the Six-Day War (1967). Gur and his troops were part of the assault force which wrested Jerusalem from the Jordanians, and which were the first to visit the Western Wall and the Temple Mount. The pictures of paratroopers crying at the Wall and Gur's audio recording in the communication networks, "The Temple Mount is in our hands!" (!הר הבית בידינו, Har HaBayit BeYadeinu!), became one of the most touching symbols of the war to the Israeli public.
After the war he was promoted to Brigadier General's rank and was appointed as the IDF commander in the Gaza Strip and northern Sinai Peninsula. In 1969 he was promoted to Major General and was appointed as the commander of the northern front, where Palestinian terrorists from the PLO, backed by Syria attacked Israel's northern settlements. Gur led several counter-attacks to reign in the terror attacks, conquering the Shebaa farms from Syria in order to establish a defensive position to prevent border attacks.
From August 1972 to December 1973 he served as the IDF military attache at Israel's Washington D.C., embassy. In January 1974 he was reappointed as the commander of the northern front.
Area 21, a military base in the Sharon plain, was named in his name (Camp Mota Gur).
Following his retirement from the IDF, Gur was appointed as the general manager of Kur Mechanica company. In 1981 he was elected to the Knesset as a member of the Alignment. Re-elected in 1984, he served as Minister of Health and was also a member of the Knesset's Security and Foreign Affairs Committee. Between 1986 and 1988 he served on the board of Solel Boneh, a construction company. In April 1988 he was appointed Minister without Portfolio, a position he retained following the 1988 elections until March 1990, when the Alignment pulled out of the coalition.
After Labour (which the Alignment had merged into) won the 1992 elections, Gur was appointed Deputy Minister of Defence, responsible for of preparing the Israeli economy for times of war and crisis and interacting with the Jewish settlers in West Bank and Gaza Strip.