Thats very unclear. No one knows anything about your financial circumstances so its not possible to confirm that whatever you want to do would be better for the lender.
Do you mean that you want to take over from the guarantor and have the guarantor released?
Or do you mean you want to be joined on the mortgage and be a mortgagor and have the guarantor released?
Or do you mean you want to be an owner of a one half share and have joint responsibility for the mortgage and have the guarantor released?
Whatever you want to do, you can only do with the agreement of the lender ( or a new lender if you intend to change mortgage lenders) and only the last option has any tax/ftb issues attached.