I'm not sure exactly what you are after... but this prevents multiple view button pushes, closes the subwindow, and resets the view button. The downside is needing subwin1 to be a global, but that is good anyways for memory reuse of the subwin1 object.

#!/usr/bin/perl -w
use warnings;
use strict;
use Tk;
use Tk::FileSelect;

my $mw = MainWindow->new;

$mw->configure( -background => 'black', -foreground => 'white' );
$mw->geometry( "400x100" );
$mw->title( "Multiple Windows Test" );

my $button1;
my $subwin1;

$button1 = $mw->Button(
   -text       => "view Results",
   -background => "cyan",
   -command    => \&button1_sub
)->pack( -side => "right" );

$mw->Button( -text => "Exit", -command => sub { exit } )
 ->pack( -side => "bottom" );

sub button1_sub {
   $button1->configure(-state=>'disabled'); 
   $subwin1 = $mw->Toplevel;
   $subwin1->geometry( "500x400" );
   $subwin1->title( "Sub Window #1" );

   my $fh;
  open( $fh, '+<', "./test.txt" ) or die $!;
   my @contents = <$fh>;
#   print "@contents\n";
   close( $fh );

  my $sublable = $subwin1->Scrolled( 'Text', -scrollbars => 'osoe', )-
+>pack;
  $sublable->insert( 'end', @contents );

 my $subwin_button = $subwin1->Button(
      -text    => "Close window",
      -command => [$subwin1 => 'destroy'],
    )->pack( -side => "bottom" );

#=================Creating save buttion on subwindow ===========

my $save_button = $subwin1->Button(-text=>'save',
   -command =>\&get_save, -background =>'cyan')->pack(-side=>'right');
}

MainLoop;

sub get_save {

        my $dst  = $mw->getSaveFile(
            -initialdir       => '/root/',
            -defaultextension => '.in',
            -initialfile        =>'test.txt',
             -title            => 'Save',
            -filetypes        => [
                [ 'myfiles'    => '.in' ],
                [ 'All files' => '*'    ],
            ],
        );

      $dst ||= '<undef>';
      warn "dst=$dst";
  
     $button1->configure(-state=>'normal'); 
     $subwin1->withdraw;
}
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