The phrase expel isn't really used any more,
They say either temporary or permanent exclusion.
So with students who have needs similar to your daughter's, it is common for schools to ask parents to take the child home if the child is distressed.
Legally this is not permitted - it's an illegal exclusion because a student should be in school unless illness/school trip etc and if they have asked you to take the child home the only legal reason is because they have been suspended/temporarily excluded.
If the child has been suspended/temporarily excluded there is usually paperwork and at least in secondary it is usual for there to be a meeting with parents, child and pastoral team (re-integration meeting) to discuss the situation.
Dfe advice for parents here:
www.gov.uk/government/publications/school-exclusions-guide-for-parents/a-guide-for-parents-on-school-behaviour-and-exclusion#what-happens-if-your-child-is-suspended-or-permanently-excluded
Obviously this is problematic and you are now stuck between two bad places because if you take her home they record it as unauthorised absence and if you don't they'll suspend her and you take her home and she has a suspension on her record.
In terms of the EHCP, the more suspensions on her record the more obvious it is the school are not meeting need and therefore she needs additional support,
Schools can permanently exclude (expel) a student, and it is possible to do this for repeated behaviour that triggers suspensions. Most schools try hard not to do this with SEND students (unless it really is incredibly obvious that needs are not being met and the student is putting themselves and others in danger).
If the school does this, there is a lot of paperwork and you do have a right to appeal. The local authority then takes on responsibility for her education (after I think 5 or 15 days) and needs to find her another school.
Many counties have agreements not to permanently exclude (expel) and will instead do what is called a managed move where they essentially swop a student with another school. So your child would have a different school they could try.