The "interest rate cut" to which you refer is the ECB refinancing rate. It is the rate the ECB charge for collateralised loans at their "refinancing window".
So, If you are an approved user of the refi window and have some acceptable collateral to place, then this "interest rate cut" is yours to have by going to the European Central Bank window.
If, on the other hand you borrow from a commercial bank, you will need to either rely on the terms of your loan contract (maybe it is linked to the refi rae as a tracker) or on the potential indirect effect that this refi rate reduction might (might) have on the cost of funds to your bank and/or other competing banks.