If your wife has only a PRC passport, my understanding is she will not be allowed to enter Taiwan at all.
If your wife has another passport, she will be allowed to enter Taiwan as a tourist, but will have to leave every six months to get a new tourist visa. This is because, in common with the PRC government, the ROC considers all people with yellow skin born in China to be “Chinese” regardless of their actual nationality. Your wife will have no residence permit, no ARC, no Jian Bao card (National Insurance) and will have to get a new visa if she leaves Taiwan and wishes to return. You might be aware (and if you’re not, a couple of days with your wife in Taiwan will be enough to impress this upon you) that mainland Chinese women in Taiwan are universally regarded as prostitutes. This means that you will have to accompany your wife to the visa office each time she gets a visa to pre-empt the sort of crap she is likely to have to put up with were she to go alone. So, holidays become a real pain in the arse involving as they will do, a stop in the nearest city to needlessly apply for a new tourist visa.
If you can prove that your wife has resided (dingju) outside the PRC for four years without spending more than 30 days in the PRC during any of those years, she will be allowed (in theory) to get a resident visa and ARC.
I have been unable to get my head around the ease with with the ROC government defines such people as being (a) foreigners for the purpose of issuing a tourist visa in a non-PRC non-ROC passport; and (b) “Mainlanders” for the purposes of refusing to issue a resident visa. But it does, and is blissfully uninterested in the offence and inconvenience this causes. Naturally enough, those who make these policies are quite happy to accept the citizenship of the USA, Canada, Australia, etc. when it suits them.
It is also interesting to note that the law under which visas are issued states that anyone intending to stay for more than six months should apply for a resident visa. It doesn’t say “except people who were born in China who must apply in perpetuity for six-month tourist visas”.
The British government says my wife is British. The PRC government says my wife is British, and that she is not a citizen of the PRC (and they have issued documents to that effect - in fact they revoked her PRC citizenship). The Taiwanese government appears to say that she is sort-of British, but not British enough to get a resident visa, as well as being a citizen of the ROC (under the Constitution), but not one who can live or work here, as well as being a dalu diqu renmin (whatever that means - as she does not have household registration in China she doesn’t fall under the definition of Dalu Diqu Renmin in the law but hey, who cares what the law says). Of course had she been white (or black) that day when we applied for her resident visa at the Ministry of Foreign Affairs, the issue would never have come up. Oh well.
I wouldn’t recommend bringing your wife here unless she has a foreign passport, gets her residence visa before setting foot in Taiwan, and doesn’t mind meeting a significant number of uneducated small-minded fuckwits, who haven’t been further than the end of their own street, thinking that because she’s from China she’s a whore or some social misfit’s mail order bride. You have been warned.