I have about a 3/4" tear in the insulation of my transducer cord. I know large tears in the insulation can cause interference. The inner wire is barely exposed. Will this cause interference and do I have to buy a new ducer again?

You might repair it with liquid rubber or it can be spliced and sealed with shrink tubing.

If by the inner wire you mean the braided ground shield wire which is wrapped around the inner conductor, no it won't cause interference.  If that braided wire has been damaged it could cause an impedance problem which could give false readings.  Otherwise,  follow Jig mans advice.  

Give it time to dry out well and apply a couple of coats of this.

http://www.plastidip.com/industrial_solutions/Liquid_Tape_-_Electrical_Insulation

Give it time to dry out well and apply a couple of coats of this.

http://www.plastidip.com/industrial_solutions/Liquid_Tape_-_Electrical_Insulation

X2 Great product. I repaired an electrical harness on a saltwater boat 5 years ago and sealed the repair with it. It works.