How about:

use Data::Dumper;

open(DAT, "< file") or die $!;

while(<DAT>) {
  chomp;
  push @data, [ split( /,/ ) ]; # or split( /,/, $_ )
}

print Dumper \@data;
[download]

The while loop reads line by line, so it takes care about the splitting on newlines already.
The split on comma is inside square brackets - these create an anonymous array around the results of split.
That array is pushed on  @data.

Cheers, Sören