There is no API for doing that. When you view your own image in the webbrowser there is a link to download the original version. You can probably automate that, but there is a lot of uncertainty if you are allowed to do that or if Mapillary will throttle the download.
I suggest you contact Mapillary regarding such concerns. They may have a download all option in one of their paied versions.
Anyway, I strongly suggest that you always keep at least a copy and a backup. Any cloud service can go away at any time, and then a good contract is worth less if the data is gone.