How did the Roman Punishment "cross" became a holy symbol to Christians? The Romans used the cross as punishment to those who didn't follow Roman laws &amp; principles.
How then did the Roman punishment "cross" became a holy symbol to Christians?
In mosaic law the Priests would offer sacrifice and do this on a table, the table was referred to as an alter.  Christ who offered himself up as a sacrifice for all, offered himself up on a Cross. His symbol is often referred to as a tree.  

In the Catholic Church when you enter into the sanctuary you bow down to three places mostly. First to the tabernacle (if the candle is lit, at the last few days of lent the Lord is removed from the tabernacle). You bow there with adoration as if (because he is there) you are bowing before Christ himself.  Then to the alter of sacrifice which is a veneration rather than an adoration,  and then to the cross itself as if to aide in your mind the fact that where you stand is Calvery at the foot of the Cross with Mary the Mother of the Lord, where Christ continually offers himself to God The Father daily. Not a new sacrifice but he same sacrifice re-presented.

Being Holy means being set apart. A cross used by Roman executioners means nothing, but a cross with the Lord hanging from it now that is Christ Crucified and that is what the Church Preaches.  Anything else is simply two sticks or a cross empty of Christ.