Mammals (Mammalia) are structured (currently) like this:
- Subclass Yinotheria
- Infraclass Australosphenida
- Subclass Theriiformes
- Infraclass Holotheria
- Superlegion Trechnotheria
- Legion Cladotheria
- Supercohort Theria
- Cohort Marsupialia
- Cohort Placentalia
That is a large target.
Genetically speaking the Platypus (a monotreme under the Order Montremata) shares roughly 82% of its genes with other mammals, and has roughly two thirds the number of genes as found in a Human.
In comparison a Chimpanzee differs to a Human genomically by about 3%, although there are 35 million single nucleotide edits across the full DNA strands. There are viruses, bacteria and parasites capable of cross-species infection between humans and apes. So there is some plausibility that one of these could be evolved/engineered to target the Cohort Placentalia.
For most people wiping out placentals mammals is enough to satisfy your requirement.
However Marsupials are also mammals. They are endemic to Australia, South and North America, and a few islands. Monotremes are known to exist on the Australian continent and Tasmania alone. At least in these places a disease that wipes out mammals would need to include these creatures.
Avian Influenza is an example of a virus capable of jumping animal classes, specifically Avian to Human and back. This does give credence to a virus being capable of infecting any mammal, and being carried by another species. Birds are good for this as they can carry the disease across geographical dividers. Unfortunately they would not be ideal agents for infecting most sea-mammals.
This pandemic mammalian disease will also have to contend with a wide-scale of environments. Mammals are widely dispersed and occupy numerous environments: ocean, stream, land, cave, mountain, valley, savannah, jungle, and sky. They live in the Arctic circle all the way through to the Antarctic circle.
While this might not seem important, when not within a host, the disease must be capable of maintaining itself in the larger environment, and either seeking or waiting for another suitable host, otherwise it essentially dies with its host.
A disease that co-evolves with its hosts cannot kill all of its hosts. That would be a bad survival trait causing the disease and the hosts to die out - extinction.
A disease that jumps from one type of Host to another, has some latitude initially. After all it has a conserved host base, and the new host has zero defenses. This might eliminate a specific target host if all of those hosts were to become infected simultaneously. However nature has large barriers that tend to prevent simultaneous infection of all novel hosts - like mountains, rivers, and oceans. Thus through chance eventually the new host type will either die out, or some of their number will survive, leading back to the disease not killing all hosts.
Sexual Reproduction and genetic variability
Because Hosts have been evolving for millions of years against a back ground of infection and parasitisation. They do have a few tricks. One is sexual reproduction. This recombines genes from two parents reshuffling the genome and essentially the entire structure of the DNA. This decreases the likelihood that a disease that is effective against either parent, will be similarly effective against the off-spring.
This tends to force diseases to focus on conserved genetics, and the conserved proteins and complexes that are subsequently produced. Fortunately this allows the immune system of the animal to learn and focus defenses around these conserved areas.
Of course diseases can rage uncontrolled. There is a problem though. They need fresh meat (literally) to maintain the plague conditions.
Humans recently figured out how to achieve this with the invention of cities, and co-habitation with domesticated/pest animals. You can see this through the history books from at least Egypt on through the European medieval cities. These places were essentially death traps for humans and animals alike with disease jumping between species, but not running out of fresh hosts because more would be brought in (be they human, or other animals). The black plague is a good case in point. It was spread by the inter-city trade, but once entrenched in a city, it could last for years.
Unfortunately this mode of plague sustenance will not work for killing all mammals. Largely because many will not migrate in a sustained manner to a city, or even its cave/oceanic equivalents. But also because the Humans have learnt how to institute quarantines, and other health interventions which suppress plagues until they naturally die off.
It is theoretically possible to evolve/engineer a bacterium/parasite/virus that could be used to wipe out a given population of a particular species, or even several species/orders/classes. Numerous examples exist currently.
- There is a chance that sexual reproduction will have created at least one individual that can survive being infected
- The animals are not sufficiently concentrated to ensure that all hosts are simultaneously infected, or continual reinfected should the initial infection be defeated.
- The specific disease will have to focus on the most highly conserved areas of the genome, where the animals will have highly advanced immunological defenses.
- Humans will naturally institute quarantines, and other health measures to reduce infection and severity.
Can it happen?
- Wiping out a group of individuals is possible - it happens often enough see the spanish flu.
- Wiping out a species will be difficult, but not unachievable. A new species in a small environment would be simplest, any geographically diverse or separated species complicates maters.
- Wiping out a Cohort, Order, or Class is supremely difficult as conserved sequences are already well tested for vulnerabilities, but if such did exist universal extinction would require a near simultaneous infection, and a plague supporting environment. Essentially a high concentration of all targeted hosts, which maximises reinfection of any survivors in order to overwhelm immunological defenses, and supports chances for cross-species infection from a carrier host type.