Wissell was born in Göttingen, Province of Hanover. He was a member of the SPD from 1888, and belonged to the right wing of the party. From 1908, Wissell was a member of the central workers' secretariat of trade unions in Berlin. From 1916 he worked part-time in the SPD newspaper Vorwärts.
In March 1918, Wissel was elected to the Reichstag for the electoral district "Potsdam 6"; he remained a member of the Reichstag until the collapse of the monarchy in November of that year. On 28 December 1918 Wissell was called to join the Council of the People's Deputies, along with Gustav Noske. The appointments came about after the three representatives of the Independent Social Democratic Party of Germany (USPD) had withdrawn from the Council. This opened an opportunity for the SPD to send more delegates to the Council. During the revolution, as Second Chairman of the General Commission of Trade Unions, Wissell also called for an arrangement with employers, and opposed the formation of a Soviet republic. One result of his arguments was the conclusion of the Stinnes-Legien Agreement, which meant that the employer's associations for the first time recognised the trade unions as the representatives of the workers.
In January 1919, Wissel was elected as an SPD candidate to the Weimar National Assembly. One and a half years later, in June 1920, he was elected to the first Reichstag of the Weimar Republic. He was re-elected 7 times from 1924 to 1933, and was a member of the German parliament for almost exactly 13 years, from June 1920 to June 1933. The important parliamentary activities that Wissell participated in during his time in the Reichstag included the vote on the Enabling Act in March 1933: here, he was one of 94 members who voted against the law that created the legal foundations for the Nazi dictatorship. It was passed by 444 votes to 94.
Apart from his work as a member of the Reichstag, Wissell filled various high public offices in the 1920s. From February to July 1919, he was the first Minister of Economics of the Republic. In this function, he worked towards a socially controlled economy for the benefit of the community. When this plan was not successful, he resigned. From 1928 to 1930, as Minister of Labour he belonged to the Kabinett der Persönlichkeiten (Cabinet of Personalities) under Hermann Müller. In 1929, he received an honorary doctorate from the University of Kiel due to his public service.
As a politician engaged in social policy, Wissell was a member of the executive committee of the German General Trade Union Federation from 1919 to 1924. From 1924 to 1932 he was also an arbitrator in pay negotiations in Berlin and Brandenburg.
After the Nazis' rise to power in early 1933, Wissell was expelled from public life, being a prominent Social Democrat. His Reichstag membership was withdrawn in June 1933. He was also placed under arrest for 2 months. He then lived a withdrawn life in Berlin until 1945.
After 1945, Wissell worked on rebuilding the SPD in Berlin. He clearly rejected a unification of the SPD and the Communist Party of Germany (KPD). In the last years of his life, he received many different honours: in 1949 he became an honorary citizen of Berlin and in 1954 received the Großes Bundesverdienstkreuz (Great Cross of Merit). When he died in West Berlin in 1962, he was buried in a grave of honour of the Berlin Senate in the graveyard of the Protestant church Zum Heiligen Kreuz in the Berlin district of Tempelhof-Schöneberg.
Today, his name is carried by the Rudolf-Wissell-Brücke between Charlottenburg und Charlottenburg-Nord, at 960 meters the longest road bridge of Berlin, as well as the Rudolf-Wissell-Siedlung (Rudolf Wissell Settlement) in Staaken, built in the 1970s, and the Rudolf-Wissell-Grundschule (Rudolf Wissell Primary School) in Gesundbrunnen.