In order to pass arguments to a handler you need to use a closure:

parse_xml( $xmlfile);

sub parse_xml
  { my( $file)= @_;
    my $ups_able_info= [];
    my $twig1 = XML::Twig->new( twig_handlers => 
                           { 'ups:TABLE_INFO/ups:field' => sub { parse
+_table_info( @_, $ups_able_info); }
                              )
                         ->parsefile( $file);
    # now $ups_table_info is filled
  }

sub parse_table_info
  { my( $twig, $table_info, $ups_able_info)= @_; # note the extra argu
+ment
    my $table_column = {};
    $table_column->{$table_info->field('ups:tag')}  = $table_info->fie
+ld('ups:ui_name');
    push(@{$ups_table_info}, $table_column);
  }
[download]

A good introduction to closures in Perl: Achieving closure by Simon Cozens

Also, I made a few cosmetic changes to your code, mostly to make it look a bit more modern:

• no need for the & before a function name,
• you mix camel case (parseXml) and underscore separated (parse_table_info) names, pick one scheme and stick to it (also, I hate camelCase ;--)
• to me my $ups_able_info= []; is a lot more readable than my( $ups_able_info)= ([]);
• use the XML::Twig->new syntax instead of the old, and potentially dangerous, new XML::Twig
• I added the call to parsefile, to actually parse the file,
• I usually write $elt->field( 'foo') instead of the longer $elt->first_child_text( 'foo') (even if it takes me longer to type because I usually type filed first, then go back and fix it ;--(

Also, you data structure seems a bit weird to me, but maybe it makes sense, I don't have enough detail to tell. $ups_table_info will end up looking something like [ { ui_tag => "val" }, {ui_another_tag => "val2"}, ...],, which doesn't look like the easiest to use data.