When adding binary numbers, how do you just ignore the overflow?
Carry and overflow are not the same thing.

The MSB of a 2's-complement number is the sign bit. The bit you're talking about is the carry-out from the addition of the MSBs. There is an "overflow" only if the signs of the operands are identical AND the sign bit of the result and that carry-out are not identical. If the signs of the operands are different, then there cannot be an overflow, regardless of the state of the carry-out

Try a few examples for yourself to see how it works.