Mebes completed an apprenticeship as a carpenter and then studied architecture at the Technical University (Technische Hochschule) Braunschweig and the Technical University (Technische Hochschule) in Berlin-Charlottenburg. After the 2nd state examination, he worked as a government architect.
From 1906 (according to other sources already from 1902) until 1922 Mebes worked for the Beamten-Wohnungs-Verein zu Berlin eGmbH in Berlin.
Together with his brother-in-law Paul Emmerich, he ran from 1911 the architectural office Mebes & Emmerich, which was mainly dedicated to housing development. They also designed schools and administrative buildings.
On 19 November 1920, he was awarded an honorary doctorate (Dr.-Ing. E. h.) by the Technical University of Braunschweig on the recommendation of the Department of Architecture. After leaving the Beamten-Wohnungs-Verein, he influenced and organised large housing estates for non-profit housing associations in Berlin ("Siedlung am Heidehof" in Zehlendorf, "Friedrich-Ebert-Siedlung" in Wedding, "Spreesiedlung" in Oberschöneweide or the "Siedlung Rauchlose Stadt" in Steglitz).
In 1931 he became a member of the Prussian Academy of Arts, but after the National Socialists seized power he was expelled again on May, 15 1933. Mebes reduced the size of his architectural practice.
However, Mebes & Emmerich remained employed after 1933, for example on larger Gewobag housing estates in the "Reichsforschungssiedlung Haselhorst", the Flußpferdhofsiedlung in Hohenschönhausen and Rüstungsfacharbeiter housing blocks in Tegel-Süd.
He is buried at the Berlin-Zehlendorf cemetery.