TDR is the right tool to determine the position of a cut, squeeze or short.
A TDR will not tell you where the wire is. So use a tracer to determine the route of the wire (if you don't have pictures), and use the TDR to know where the damage is along the route.
Issues that may murk the waters:
- The TDR needs to know the velocity factor of the wire. If you have a sample, you can confirm it with the TDR
- Hooks (short radius turns) near the point of damage may throw the measurement off, and the accuracy then depends on the sophistication of the TDR (pulse based, or correlation based).
Despite this, the method is very accurate and commonly used in telecom.
The TDR relies on a correct input of the Velocity Factor "VF" of the wire. For data wires it's in the range of 80% to 60% of the speed if light. (Maybe this is obvious, but for the general reader I'll add that this is not to be confused with the "data speed", as the two -data rate and propagation speed- are generally not related). A "faster cable" has to do with bandwidth and losses/attenuation, not the velocity of electromagnetic waves (although, the two are often related).
I'm not sure how familiar you are with how a TDR works, or whether the TDR you have in mind uses pulses or correlation sequences, but it all comes down to measuring the time delay of an electromagnetic reflection that bounces of a damaged, open or shorted section of wire.
The distance is calculated from the reflection, based on the electromagnetic propagation speed.
And the speed depends on the type/size/materials of the wire and to a small degree how it is deployed, and this is where a bit of uncertainty comes into play.
TDR with a Pulse or a Sequence
If the TDR uses pulses, then the shape (roundness) of the received pulse -due to the wire- will add some uncertainty, and a correlation based TDR would perform more accurately. A correlation based TDR sends a pulse train, and matches that against the received pulse train. It's very accurate even if the received pulses are rounded and otherwise reshaped. With a single pulse it's far more difficult to determine the delay if the pulse is rounded or reshaped.
Alternative to TDR
If you don't have a TDR (they are expensive), maybe it is more likely that you can borrow, from a friend, a scope and signal generator to perform a frequency sweep and obtain the reflection points based on the spectrum. You'd have to borrow the knowledge as well, to perform the right measurement and translate the result to a distance.
Practical Wiring Consideration
Remember, if you are cutting a hole in the drywall to confirm & fix the damage, you'll likely have 1ft of length exposed anyway, so depending on where the detected damage falls relative to any framing & passages, the accuracy can be moot (if you can cut a 12in x 12in hole) or critical (whether it's upstairs or downstairs).
You can calibrate the distance -reported vs actual- by letting the TDR measure the length of a sample of an open ended wire. Compare it to the actual length of the sample, and the relative difference (e.g. in %) is your adjustment factor. This works for well for minor adjustments well under 10%.
Use a sample of exactly the same wire (brand, type). Unroll it, and use a length that's close to the length of your install, down to maybe 1/8 of it if you don't have enough or if it's cumbersome, but do not use just a tiny left over cutting.
The calibration corrects for any discrepancies between the reported and the actual VF of the wire, so that you can be more confident about where the damage is, relative to your walls, floors etc..
VF vs Z0
As a side note, the Velocity Factor and the Characteristic Impedance Z0 are not the same thing but they are closely related to the physical properties of the wire (dimensions, conductivity, dielectrics). Just to note: "Z0" is not the resistance of the wire; so don't measure it with an Ohm meter and somehow try to calculate or correct the VF from it.
As with anything behind finished walls, luck is a factor, but remember the words of Edna Mode: "Luck Favors the Prepared".