And putting together all of what the others have said ( and adding some sanity checks I follow when things start going wrong ) :

use strict   ;
use warnings ;


sub del {

    my ( $delroadName, $delroadNumber ) = @_ ;  # This line handles pa
+rams for function, 
                                                #    moved to first pa
+rt of function

    my $process_file = "data.txt";              # Variable name change
+d to reflect action - 
                                                #    This kind of thin
+g can mess things up later. 

    my @data ;
    { 

    # Adding additional scope to prevent missuse or error use of fileh
+andle.

    open( my $data_file_handle, '<', "$process_file" )   # Changed to 
+3 param open and replaced bareword file handle.
        or die("Can't open file: $process_file");        # Changed || 
+to 'or' in case someone removes brackets for 'open'
                                                             #   Also 
+added file name to error message.         

    @data = <$data_file_handle> ;               # NOTE: 'my' removed t
+o ensure scope. 
    close( $data_file_handle );
    }



    chomp( @data ); 

    open( my $out_file_handle,'>', $process_file ) 
    or die("Can't open file: $process_file"); # Modified as above.

    foreach my $line_from_file ( @data ) {                     # Chang
+ed from for to foreach removed dependence on $_ 
    my @field = split( /\:/, $line_from_file );           

    # next if( ( $field[0] eq $delroadName ) && ( $field[1] == $delroa
+dNumber ) ); 
    # Added brackets and changed $field[0] in both to [0] and [1]
    next if( ( $field[0] eq $delroadName ) && ( $field[1] == $delroadN
+umber ) ); 
    print $out_file_handle $line_from_file, "\n";         # Modified t
+o print to file handle - Else the file will be truncated
                                                #   Since you are open
+ is with '>' and will remain blank. 
    }

    # close $output;
    close $process_file;  # You want to close the file handle, not the
+ string.

}
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Update: Corrected stupid mistake as pointed out by tobyink below.