I think that the compassion you describe is the christian form in which one great hero die for us all, taking away sins.
Hi Vimala,
from my experience you may find that compassion becomes a natural by product of your practices, for me it came after i began to practice samyama, it was divine love moving outwards and suffering going into an emptiness of inner silence within me.
The Christian compassion i believe can be achieved by anyone who is on the path of bearing the karmas of others in order to relieve suffering but i don't know the mechanism or mantra for that. You may have heard of enlightened beings who instead of healing others specifically they begin to absorb the physical emotional suffering of others and die as a result (but because there personal burden was so light they are able to help greatly)
When i practice compassion it does not create suffering for me but rather i become aware of my or others suffering and i give it to my higher self and thus it is relieved.
unconditional love is very helpful which can comfort others and when directed inwardly to the ego can turn to bhakti which will purify steadily our egos. Our desire to help is our karma yoga i.e. doing good for others. But what mechanism do we choose to take away the suffering? It can be very practical i.e. putting a bandage on the wound or buying the starving person a sandwhich, but when it comes to things like grief and sadness how do we take the suffering away?
I hope this helps to clarify what i mean by compassion
joe