So the OP issue is not genetic mutation, which obviously does happen within species, but whether or not it can be demonstrated by evidence to be the cause of origination of new species. Can micro-evolution within species be demonstrated by evidence to be the cause of eventual macro-evolution leading to new species?
It's a scientific assumption and there are scientists like
 Rupert Sheldrake and others who do not not agree that random chance is the cause of the universe. Everything is open to falsification. Scientists like 
Tom van Flanderen look at alternative theories to Einstein's gravity, and the speed of gravity, as a source of dark matter and dark energy.
Science is open to question and falsification. Abiogensis and speciation by genetic mutation are a result of the need to show that the universe and intelligent life are the result of random chance. There is still no evidence for either. There may be more to it, and honest scientists will acknowledge that, imo
There can be no chance calculation from the fact of a single occurrence, but after 1.5 billion years of prokaryote bacterial life on early earth, something happened which had never happened even once in all that time before -- and which has never happened again in all the following 2.7 billion years – although the opportunity has continued to exist for it to happen again and again, zillions of times over.
The ’miracle’ event was when a 
bacteria combined with an 
archea by 
endobiosis to give rise to the ‘modern’ eukaryotic cell. It happened only once, and without it there would be no higher life on earth. Bacteria and archea continue to swarm daily in staggering numbers, but they have never even once again combined to originate a eukaryote cell. It was a one-off, once only occurrence in the entire 4.2 billion year history of life on earth.
This is fully accepted as current mainstream science, to the best of my knowledge.