I have an investment (Rental property) on my home mortgage. How can I convert this to a separate mortgage?

Not sure I understand your question. You have taken out a mortgage secured against your primary residence for an investment property but now you would like transfer that mortgage from your primary residence to your investment property?

If I am reading this right, you have a mortgage on your primary home that you used to finance a rental property?? Contact a local mortgage broker in your area for assistance. You should be able to simply get a loan against the rental property, and use that money to pay off the loan on the primary property.