Although the reply threads go all over the place on various subject matter, the question was "how can you dissolve borax slag in order to recover dispersed fragments of metallic value " (don't worry about the diamonds, they will be just fine, as long as you do not introduce excessive heat and/or hydrofluoric acid)......... this is a common gold-extraction processing problem, absent the diamonds).
Borax is water soluble. The ancient rule, "water verses anything, water always wins", can apply here if you have the time to wait. Boiling water works faster. It is always nice to use non-toxic methods that do not obscure your metallic results. Acetic acid (vinegar) is a little quicker method which I use frequently especially when I need to step-wise microscopically examine the slag for melting characteristics (ie how well the melting process proceeded and what metals might have been in the rock - especially Platinum and Iridium).
So, usually after a rock-extraction melt (quartz, feldspar rock containing gold, silver, copper), where you add lead oxide and let the melting /heating process proceed in order to burn-off unwanted metals - the recovered fragments of metal left in the slag may not be in nice, neat buttons. What you might have is thousands of tiny fragments of gold/silver. Once you dissolve-off the slag, wash away all the acetic acid with water - then you can add nitric acid 70% to the container holding the thousands of tiny gold/silver metal fragments - nitric acid will dissolve the silver and remaining copper - leaving fairly clean gold. Once nitric acid treatment completes, wash off the gold and either melt it or dissolve it in aqua regia for a re-recovery purification.