I am looking for an equipment (like a printer) as output device of
computer to cut digital images  on metal which size is about 2X3 inchs
or less. The images look like laser cutted without color.
Please help me on who is manufacture, where I can buy it and how much the cose is.

The process you are looking for is laser etching. One manufacturer of
the equipment, and a description of the process, is at
http://www.epiloglaser.com/laser_marking.htm

Their smallest system is described at
http://www.epilogmini.com/

The website gives costs as "Lease-to-own payments through some
companies start as low as $202 a month"

As this type of equipment is widely used for personalisation of gifts
and industrial marking and sign-making, even if the lease or purchase
of such equipment is beyond your budget, you should be able to find
someone with such equipment who would undertake the marking from your
output files.

Owain