Isolating the vasculature of an organ?
The typical name for this technique is "corrosion casting" - if you search for literature on corrosion casting you will find many many papers detailing the technique. Another answer mentions "plastination" but I don't think this is really what you are looking for; plastination is a technique for preserving the tissues themselves (though the "Body Worlds" exhibit that post references also uses corrosion casts extensively).

Briefly, in corrosion casting, you gravity or pressure-fill the vasculature with a plastic, typically acrylic. It is best if the vessels are flushed free of blood before injecting the plastic, with saline/PBS, for example. (Organs from a butcher will work fine but you will get better results if you can administer heparin premortem to prevent clotting, which of course is not possible for a meat animal.) The acrylic cures, and then the tissues that remain are digested with a basic solution, ranging from 0.5 M NaOH to 6M KOH depending on the protocol (lower concentrations or NaOH will digest more slowly, higher concentrations or KOH will digest more quickly), often at elevated temperature (~37C). Note that this solution technically digests all of the vasculature as well, but you have already filled the vascular lumens with plastic, so that is what you are left with.