Never use sleep() in a Tk (or any gui ) unless it is in it's own thread. Here is how I would do it, use a timer.

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

my $timer;

my $mw = MainWindow->new();

$mw->Button(
    -text    => 'Start',
    -command => \&start_process
)->pack;

$mw->Button(
    -text    => 'Stop',
    -command => \&stop_process
)->pack;

MainLoop;

sub start_process{

my $count = 0;
$timer = $mw->repeat(1000, 
   sub{
      if ( $count < 10 ){ $count++ ; print "$count\n";} 
      });
}

sub stop_process{
#stopping the process
$timer->cancel;
}
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