My guess is, the output from the Mesa is line level, which is much hotter then mic or instrument level.
A standard 1/4 TS (instrument cable) is what you'd use however, sending a line level to a mic or instrument level input on your interface will most likely result in distortion and could damage the pre-amp on your interface.
Best practice is to level match, meaning, send a line level signal to a line level input, mic to mic etc.
Mic levels are the weakest, instrument level is stronger and line level signal is the strongest.
It can be 1,000 time greater then mic level.
I suggest digging up the manual on your interface for instructions before you plug in.
See if it can accept line level input.
If you send a mic or instrument level to a line input, nothing bad will happen, it just might not work because the signal is too weak.
On the other hand, sending line level to a mic input is not good because it's too strong.