I believe CAT is calculated on the market value less costs, liabilities, expenses and consideration.
That suggests to me that if you transfer a half share in the property to your partner, subject to her assuming 50% of the mortgage (the consideration for the transfer), then the CAT or Gift tax will be charged on the market value of the half share, less the half mortgage, and less the Stamp Duty payable, and legal fees etc. In effect, she will be "paying" a half share in the mortgage for the privilege of owning a half share in the property.
So say the half share is valued at €150,000 and half the outstanding mortgage is €130,000, legal fees and SD are €10,000 (a guess!), then the taxable value is €10,000, which even allowing for the reduction in thresholds recently is below the lowest, so there should be no CAT payable. SD will though I think.
I stand to be corrected about the above, and would love to know if I am right or wrong in my assumptions.