High fuse DE, 11011110 vs D8, 11011000, would only affect the Boot size. (512 bytes or 4096 bytes)
How are the low fuse bytes set? That has the divide by 8 bit and the clock source bits.
Does the mini have an 8 MHz resonator or a 16 MHz resonator?
The Programmer needs to connect to Reset, Power, Gnd, SCK (D13), MISO (12) and MOSI (D11).