Yes, you can easily crop collars in various ways using the Cropping options tab accessible via the Options dialog for layers from the Control Center. You can crop via lat/lon boundary, polygon, native coordinate boundary, etc.
Once your data is positioned properly, mosaicing is automatic, data will automatically line up at the proper location and can easily be exported as new combined files in a seamless manner.
Let me know if I can be of further assistance.
Thanks,
Mike
Global Mapper Support
support@globalmapper.com