Once you’re baptised, you can’t get un-baptised. The historical fact that you were baptised cannot be changed; it will always be true that you were baptised. This is what the Church doctrine means when it says that baptism imparts “character”, that is, an indelible mark on your soul. Indelible means indelible; nothing can remove it; not sin, not excommunication, not even eternal damnation. A baptized person who falls from grace and dies impenitent will spend eternity in hell with the indelible mark of baptism as an eternal reminder that they should not be there.
Related Catholic Trivia: The Roman Catholic Church accepts the baptisms of many non-Catholic Christian denominations. Rather than listing them here, suffice it to say that any baptism performed with water, and with the intention to do what Jesus intended, and while saying the words “I baptise you in the name of the Father and of the Son and of the Holy Spirit” (or equivalent words), is a valid baptism. When an unbaptised person wishes to join the Roman Catholic Church, they are baptised of course, but when a previously baptised person joins, they need not be “re-baptised” (see above!). Sometimes it happens that a convert is not sure whether they were baptised or not, or is not sure whether their baptism was valid. In such cases the words are modifed slightly to: “If you have not already been baptised, I baptise you...” etc. This is called “conditional baptism” and is only necessary because nobody can be baptised twice.
Q: If somebody gets excommunicated, don’t they need to get baptised again to rejoin the Church?
A: No. Excommunication doesn’t “kick out” a person from the Church; it is merely a formal statement that he has committed sin so great and scandalous that he is forbidden to receive the sacraments (except for Reconciliation) but he is still a member of the Church. As soon as he is absolved of the sin (and the excommunication) in the sacrament of Reconciliation, he is in “full communion” with the Church again.
Q: Why does the Catholic Church accept baptisms performed by churches that are staunchly anti-Catholic?
A: There is only One True Church; only one Universal Church founded by Jesus Christ. Valid baptism makes you a member of that Church; it does not make you a member of some particular Christian denomination (e.g. Lutheran, Anglican, etc) or some particular Catholic Rite (e.g. Roman, Eastern Orthodox, etc). Therefore, we accept any valid baptism... because God’s understanding of “The Church” is infinitely greater than our outrageously parochial understanding (no pun intended).
Q: I was baptised Catholic, but now I want to quit. Can you help me get excommunicated? [I actually received this request by email! -jkh-]
A: You know how some states and countries have legalized “physician-assisted suicide”? Apparently, it looks like you want “priest-assisted damnation” as well! Fortunately, it is a physician’s God-given duty to protect life (and not to help people die); likewise it is a priest’s God-given duty to help save souls (and not to help them be lost)! So, no. [I suspect that he knew this, but was just trying to get me riled up. -jkh-]