If I understand you correctly, it's not the fruit that is infected with fungus but the tree itself. In which case, the following applies: It's probably too late to save the tree, because the fungal hyphae (meaning the actual web of fungus) spread on the inside of the tree. That means you can't see exactly how far advanced the wood penetration process is. However, you could try targeting the specific areas that are affected and cutting them out. In the medium to long term, and depending on the intensity and progress of the infestation, you can expect the tree to start dying. During this time, please be aware of road safety, ensuring that any broken branches won't hurt anybody or anything. If the tree does not present any danger, you can let it remain standing for as long as you like.
In theory, you will be able to plant a new fruit tree in the same place — but go for a pomaceous fruit rather than a stone fruit. The new tree will also grow better if the soil in which it is planted is loosened and improved as deeply as the roots will spread (for example, and depending on the soil, by mixing in a little lime, some horn meal and some compost).
One more tip from me: If you cut the mirabelle plum tree back with a saw or shears, disinfect the blade with spirit. Otherwise you run the risk of transferring the fungus to other trees on the blade. The best-case scenario would be if the fungus were specific to its host (if it infects only mirabelle plums or stone fruit trees). However, many tree fungi are not host-specific and can infect other garden shrubs — and you may only see the effects in ten years' time.