The standard Brita pitcher filter is a mix of granular activated carbon (from coconuts), and the ion exchange resin you talk about.
Because adsorption is a consequence of surface energy and weak bonding, I believe it's considered to be a chemical process, not a mechanical one.
Adsorption is due to weak bonds that form between molecules of a surface and a fluid. AFAIK this bond is not a 'new' chemical bond since it does not break / replace existing chemical bonds in both the adsorbed molecule and surface molecules.
Rather, in the case of carbon at least, the 'bonds' are the van der Waals forces.