I would imagine that the largest cost of educating / caring for children with the highest needs is staffing.
Providing constant 2-1 or 3-1 care is very expensive. You probably need 9-10 staff to cover 2-1 24/7, perhaps even more to cover sickness etc. Of course many children will spend a lot of time at home but there are small numbers where that really isn't possible / desirable.
Many of those staff won't be well paid as it is. At least some need to have some level of teaching experience / specialist skills in order to actually provide an education.
If you try to cut your staffing bill an obvious way is to reduce the ratio. That probably puts your staff and / or the child in question at risk and may mean that you simply can't recruit for the roles. I don't think 2-1 / 3-1 rations are generally provided unless that is really required in order to keep everyone safe and it is extremely rare for 24/7 care to be provided at school.
Of course staffing isn't an absolute cost to the government. It creates jobs and staff pay taxes, which feed back into the system.
A second cost for some children will be specialist equipment and / or adaptions to buildings so that they can access it. The issue with this is that much of the technology / adaptions will be bespoke, which makes it expensive. If everyone needed a specialist wheelchair they would be relatively cheap but anything you are making for a small market is expensive. I think the cost of some assistive technologies is falling as they are used in the mainstream in smart phones etc. e.g. eye tracking technology.
There may be some discretionary spending e.g. do you provide a swimming pool which all children at a special school can access. You can provide an education without it. But the swimming pool only really provides for disabled children what other children would get anyway and may be of higher benefit to the disabled children e.g. because of the health benefits or because they cannot access other local pools. The special schools near me rent out their facilities as much as they can for classes and so on.
I'm sure there are inefficiencies and maybe it would be preferable for local councils or the government to provide more special school places than to rely on the private sector (though using the private sector sometimes seems to be more cost effective overall for the government even where individual cases look to be very expensive). Maybe placements for very high needs children should be centrally funded, so you don't get a situation where some the budgets Local Authorities are really affected by having to fund them, which incentivises litigation to try to reduce the cost.
But overall I doubt that special schools are spending most of their money on nice to have extras without which they could still provide a reasonable education. In my experience, a lot of the "extras" e.g. trips to local attractions or special technology is funded by charities or donors or local businesses etc.