It always bugged me that being expelled from Hogwarts meant that you could no longer be educated in magic and that your wand would be snapped in half. Expulsion is serious, of course, but magic is the defining aspect of a wizard's being and it seems amazing that a few indiscretions, especially in light of the fact that these indiscretions would be made by relatively young and immature children, would carry such a harsh penalty. The penalty would forever cut off the wizard to the world they lived in and from their family and friends, and incapacitate them in daily life, as magic is used with everything. Is there any information in the books or from JK Rowling that explains this and why it's so harsh? Is the punishment always the same? Can a wizard ever go to a new school?
There doesn't seem to be many if any examples of typical expulsion. The only examples of expulsion seem to be Hagrid, who was accused of something uncommonly serious, Harry, who was being targeted unfairly by the ministry, and Grindelwald, who was most likely of age and was also from a different school/country.