You haven't said anything about where the text is coming from or where it's going, but, as a general rule:
Processing is fast.
I/O is slow.
Unless you're doing some seriously heavy manipulation of the text, your program is probably spending most of its time reading in data from disk/network/database and writing the results back out. You can improve a bit on that (e.g., by reading data in the right-sized chunks instead of slurping the whole dataset at once or using indexing so that you don't have to read unused data at all), but, ultimately, your program can never be faster than the time it takes to complete its I/O operations.
As for the question itself, I do believe (but have not benchmarked to confirm) that using $_ is marginally faster than using a named variable. However, if your program is so performance-sensitive that this tiny, tiny micro-optimization matters, then Perl is most likely the wrong language for you to be using in the first place. Get something lower-level and compiled that doesn't waste CPU time on magic and DWIMmery.