As long as the card is RoHS compliant (and if it's sold in the EU it will be) then it'll contain very few heavy metals and should be somewhat less toxic. As such I'd probably suggest using a blender to reduce it to small pieces, then a ball mill (using stainless steel balls, not lead!) to pulverize it into dust. I'd argue online that the heatsinks and metal brackets aren't part of the card, and only eat the PCB and the parts on the PCB. Consider washing it with acetone, then soapy water, then rinsing with water to remove thermal grease and maybe some of the paints and epoxies that don't constitute the graphics card itself. Then plug it in and show it still works (briefly - before it overheats!) so people don't call foul that you aren't also eating the enclosure, fan, etc.
At that point you should end up with less than a quarter cup of powder, which is mostly glass (circuit board is fiberglass), with some copper, some gold, some silicon. The silicon will be the most dangerous part - not the silicon itself, but the doping used on it to create the semiconductor, sometimes elements such as boron. These are mostly low-toxicity to humans, but they do present some concerns.
As such, I would combine it with a very large, very basic (ie, opposite of acid) thick drink. The basic nature of the drink should counteract a lot of the acid in the digestive system, and hopefully few of the elements will find their way into your blood stream. Then I'd flush my digestive system very quickly with a lot of other food and liquids so that this graphics card smoothy spends very little time in my system.
Then I'd check my will, make sure all my affairs are in order, and hope for the best.