It can be done, though.
It can be hard to tell what you are getting, though. All google references I see to Speer African Grand Slam bullets say tungsten carbide core.
I think the Alaskan bullets of about 50 years ago had metallic tungsten cores but I no longer have the manual to be sure.
First generation KTW pistol armor piercing had tungsten alloy cores.
There was a frangible bullet design made of zinc stranded cable in a copper bullet jacket, but sintered tin-copper powder metal pretty much rules the roost.