Two Wire Cable: Two Inputs to one output
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Parallel connection of two inputs to one output.


  If I open up a guitar cable (which uses two inner wires: signal and ground) and connect the signal outputs and grounds together, could I connect that to another cable, therefore get a 2 inputs connected to one output?


Yes.

You forgot to ask would it work.

It might. It depends on what the inputs are. 


Two guitars might work but the volume controls of one will affect the other.
Two line outputs - pre-amplifiers, guitar pedals, MP3 / phones, etc., driven by transistor or op-amp outputs - may not work well as they may have low output impedance.
You may get mains hum if you create ground loops through the equipment you connect to.


The right solution is to use an audio mixer which prevents interaction between the two input signals and allows individual volume control.