We report a strong magnetic activity using an all-dielectric metamaterial based on Mie resonances, designed to work at millimeter wavelengths over the 30-70 GHz band. A good agreement was achieved between numerical simulations and experiment in the case of one meta-layer based on TiO2-disks, manufactured using a simple bottom-up approach. We also demonstrate through numerical simulations a negative refractive index within the same investigated metamaterial made of high dielectric permittivity single-size pellets. Choosing the suitable aspect-ratio of the metamaterial building blocks, a broadband magnetic response and a left-handed behavior are simultaneously obtained. This is a promising step towards innovative and complex electromagnetic functions, involving cheap and easy made metamaterials for millimeter wave applications.