Thanks for taking the time to update. Some points to review:

• Calling split_file recursively means that your stack will fill up as the number of chunks goes up. You've got one buffer per sub call, so that's probably the source of the memory usage and slowdown you reported.
• Your algorithm/logic, even though it works, is confusing, and actually can possibly go wrong: Right after you read from the file, you use $iterator to determine whether to call split_file again - I think you need to look at $len first. Keeping a running count of the bytes written to the current chunk and comparing it to the desired chunk size might be better. Also, inside the while(1) loop, you don't seem to consider what happens after the call to split_file - the loop keeps going! In fact, if the file being split is exactly divisible by the chunk size, you create one final .splitNNN file that is empty.
• This is not correct: open my $fh, '<', $_ || die "cannot open $_ $!";, since it gets parsed as open(my $fh, '<', ($_ || die("cannot open $_ $!"))); (you can see this by running perl -MO=Deparse,-p -e 'open my $fh, "<", $_ || die "cannot open $_ $!";'). Either write open my $fh, '<', $_ or die "cannot open $_ $!"; (or has lower precedence) or write open( my $fh, '<', $_ ) || die "cannot open $_ $!";
• You're still not checking the return value of read, which is undef on error.
• The code could also use a bit of cleanup. Just a couple of examples: The name $split_fh is a bit confusing, and you could append $num to it right away. In split_file you set $iterator = 0; but then don't use it in the recursive call to split_file.

I think this might be one of those situations where it would make sense to take a step back and try to work the best approach out without a computer - how would you solve this problem on paper?

But anyway, I am glad you took the time to work on and test your code! Tested code is important for a good post.

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