Dust and stars play a complex game of interactions in the interstellar medium and around young stars. The imprints of these processes are visible in scaling relations between stellar characteristics, star formation parameters, and dust properties. Aims. In the present work, we aim to examine dust scaling relations on a sub-kpc resolution in the Andromeda galaxy (M31). The goal is to investigate the properties of M31 on both a global and local scale and compare them to other galaxies of the local universe. Methods. New Herschel observations are combined with available data from GALEX, SDSS, WISE, and Spitzer to construct a dataset covering UV to submm wavelengths. All images were brought to the beam size and pixel grid of the SPIRE 500um frame. This divides M31 in 22437 pixels of 36 arcseconds in size on the sky, corresponding to physical regions of 137x608pc in the galaxy's disk. A panchromatic spectral energy distribution was modelled for each pixel and maps of the physical quantities were constructed. Several scaling relations were investigated, focussing on the interactions of dust with starlight. Results. We find, on a sub-kpc scale, strong correlations between Mdust/M* and NUV-r, and between Mdust/M* and mu* (the stellar mass surface density). Striking similarities with corresponding relations based on integrated galaxies are found. We decompose M31 in four macro-regions based on their FIR morphology; the bulge, inner disk, star forming ring, and the outer disk region. In the scaling relations, all regions closely follow the galaxy-scale average trends and behave like galaxies of different morphological types. The specific star formation characteristics we derive for these macro-regions give strong hints of an inside-out formation of the bulge-disk geometry, as well as an internal downsizing process. Within each macro-region, however, a great diversity in individual micro-regions is found, regardless of the properties of the macro-regions. Furthermore, we confirm that dust in the bulge of M31 is heated only by the old stellar populations. Conclusions. In general, the local dust scaling relations indicate that the dust content in M31 is maintained by a subtle interplay of past and present star formation. The similarity with galaxy-based relations strongly suggests that they are in situ correlations, with underlying processes that must be local in nature.