On 17 July 1932, later known in German history as the Altonaer Blutsonntag, some Communists, with Tesch among them, tried to disrupt a march by the National Socialists (Nazis) in Altona through a working-class area. Arguments and shoving escalated, culminating in gunfire that killed two SA members and 16 others, the latter group likely by uncontrolled police gunfire. Tesch, who was involved in the violence, was later alleged to have fired shots in the incident.
After the Nazis had seized power, the case was brought before the Nazi Special Court (Sondergericht) in Altona. Although the investigation turned up no solid proof of Tesch's guilt, and it could not be proved that Tesch had brought a weapon to the demonstration, he was nonetheless sentenced to death along with Walter Möller, Karl Wolff and August Lütgens. When Hermann Göring refused to commute the sentences of the four, on 1 August 1933, in the courthouse courtyard – now home to Altona's Local Court – they were beheaded. These were the first executions in the Third Reich.
All those sentenced to death had their convictions overturned on 13 November 1992 by the Hamburg State Court. Further sentences meted out by the Sondergericht in connection with the Altonaer Blutsonntag were reversed on 21 June 1996 and 29 June 1998.