To add to Dom's post...
The Viceroy (Alva de Liste) was not acting totally on his own accord when he reopened the mint. The Lima city council (the "cabildo") is said to have proposed the idea, at least there is some record of that.
During the 1659-1660 mint production denominations of 1,2 4 & 8 were struck. Total mint production is recorded as 2,685,205 pesos (8 reale equivalents). This shear quantity indicates quite a serious effort, not a novel undertaking. Most of the coins are 1659 dated, about 4 times as many as 1660.
I think the main reason That Phillip IV shut down the mint (which occurred April 1660) was that he was really caught off guard, not having known of or authorized its opening. Apparently the viceroy received quite a reprimand for his bold stretch of his authority, but I don't know the exact nature of the punishment he ultimately received. I wasn't aware that it had forced his resignation.
Stan