Global Change cannot be used to replace an existing Major or Minor with a blank entry, so the value must be replaced with another value, like Delete Me and then use the Delete Table Entry Plugin to remove the Major or Minor from the Education Relationships.  It will be a multi-step process.

1. Export the following fields from the Constituent records to a CSV file

Constituent ID or Import ID
Relationships>Education>Import ID
Relationships>Education>Majors (or Minors)>Import ID
Relationships>Education>Majors (or Minors)>Major (or Minor)

2. Open the CSV file and change the Headers to the the following values
ConsID or ImportID
ESRMajESRImpID
ESRMajImpID
ESRMajMajor

3. Change the value for the Major (or Minor) to DeleteMe
4. Save and close the CSV file
5. In The Raiser's Edge, go to Config>Tables>Major/Minor
6. Add a New Table Entry for DeleteMe
7. Go to Admin>Import>Constituent>Constituent>New
8. Select to Update Existing Records, include the file created above
9. Import this to update the Major (or Minor) to DeleteMe
10. Once the import is completed, use the Delete Table Entry Plugin to remove the DeleteMe entries from Majors