Put simply, you'll have to read in the file, process it, and then save it back out.

my( $filename, $arg1, $arg2 ) = @ARGV;

open IN, '<', $filename or die;
my @contents = <IN>;
close IN;

@contents = grep !/^$arg1,$arg2,/, @contents;

open OUT, '>', $filename or die;
print OUT @contents;
close OUT;
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This will force the first and second field in the file to match exactly the first and second arguments that you pass in.

Here's a command-line one-liner:

perl -p -i.bak -e "next if /^sandwich,hamburger,/" comma.file
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You could wrap this in a batch script or shell alias to facilitate the substitution of parameter values.

Alternatively:

perl -n -i.bak -e "print unless /^sandwich,hamburger,/" comma.file
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Another alternative is to use Tie::File. This lets you treat a file as a regular array variable. This is very convenient because it is easy to understand what is going on, as long as you are familiar with perl arrays.

use Tie::File;

my( $file_name, $arg1, $arg2 ) = @ARGV;

# open the file with tie
tie my @file_lines, 'Tie::File', $file_name or die;

# delete the first line
shift @file_lines;

# filter out lines containing 'sandwich'
@file_lines = grep !/^$arg1,$arg2,/, @file_lines;

# close the file with untie.
# IMPORTANT: always untie when you are done!
untie @file_lines or die "$!";
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Update: Note that perl does not actually load the file into the array. It only appears to do so.