Fast drying (~60 min) is useful for optimizing production processes by increasing productivity and reducing costs and environmental impacts, especially in red ceramic industries in Brazil. However, suitable clays are necessary and, currently, studies focused on the plastic behaviour of clays with compositions suitable for extrusion, especially for fast drying, are scarce. Therefore, in this study, three different clays from the same mineral deposit were studied for producing clay-based structural products via fast drying. The clays were characterized according to their chemical, mineralogical and thermal properties, particle size, cation-exchange capacity, specific surface area and open pore volume distribution. Ten formulations were developed using a simplex-centroid mixture design of experiments and their plasticity index (PI) values were determined. The response surfaces of the formulations were evaluated according to their PI, while the formation characteristics were determined according to their extrusion workability factor values. Formulations F5 (50.0 wt.% yellow clay and 50.0 wt.% green clay) and F8 (66.6 wt.% yellow clay, 16.7 wt.% grey clay and 16.7 wt.% green clay; PI = 15.5–16.6%) displayed optimal extrusion properties, followed by formulations F7 (33.3 wt.% yellow clay, 33.3 wt.% grey clay and 33.3 wt.% green clay) and F10 (16.7 wt.% yellow clay, 16.7 wt.% grey clay and 66.6 wt.% green clay; PI = 13.8–14.2%), which are within acceptable extrusion index values. Thus, the chosen formulations have significant potential for use in the manufacture of fast-drying red ceramics.