Father with mutated mtDNA- why isn't his offspring at risk?
...would then be his offspring at risk? Why?


No. Generally speaking, fathers do not pass on their mtDNA (Mitochondrial DNA).

Why? Because the mitochondria present in oocytes (egg cell) is the mother's, as every oocyte directly inherits the mother's mitochondria when they are made in the reproductive organs. The mitochondria that the sperm from the father carry to the egg do not enter the egg cell or are destroyed in the process.

It's also worth mentioning that, in general, mtDNA does NOT reside in the nucleus of cells, but in the mitochondria itself. It is not condensed during cell division, it is not spliced during Meiosis II, and it does not undergo recombination with another cell's mtDNA. Instead, when a cell divides, each cell takes about half of the mitochondria present in the cell and maintains them. That way only the mitochondria present in the cell before division will be inherited by the daughter cells, and thus only the maternal mitochondria present in oocytes (egg cells) before sperm instigate cell division will be inherited by any offspring.