Could random male-only-offspring mutation wipe out a species?
It has happened the R2D2 mutation in mice is famous for it, the mutation prevents or drastically reduces female offspring.  It can wipe out entire populations when it shows up, it doesn't wipe out the species becasue there are frankly too many mice, separated by too much distance, while breeding too fast for the gene to spread fast enough before the population crashes. If mice happened to live on only one island however they would be gone. These events are called selfish sweeps or selective sweeps that result from a transmission bias in a gene. 

the opposite can also occur (female only) however this is slighly less likely to lead to instant extinction since a possible out exists. Lepidodactylus lugubris(a gecko) being a famous example and is a female only species that reproduced through parthenogenesis. These types of species are exceedingly rare and have problems however as they are very vulnerable to disease since they have low diversity. Species like this are driven extinct indirectly by the mutation that led to a female only species as their diversity sufferers drastically so disease or environmental change can wipe them out more easily.