Does any one knows how to go through a directory of *.txt file(s)

glob or if you need to recurse, File::Find (or File::Finder or File::Find::Rule). Or if you like to reinvent the wheel, then opendir & C. (IMHO often cargo culted, but that's just my MHO...)

check if the files found are larger than 1MB

-s

if they, are cut the file(s) into part(s)

Check perldoc perlfunc for "Functions for filehandles, files, or directories" and "Input and output functions". In particular I see two possibilities, fundamentally:

1. use sysread;
2. put a reference into $/, e.g. $/=\0x1000_000;

try putting everything together and if you have problems then show us your code.