Under what conditions can one rip on shabbos? Ex: opening up a box of tissues or an unopened item that is is gift wrapped.
The laws of ripping on Shabbos are complex.
In general, there is greater leniency in tearing a box in order to reach its contents, as we see from the Yerushalmi (which all Poskim cite) whereby it is permitted to tear a leather cover in order to extract the contents from a wine barrel.
The same will apply to tearing a box of tissues to reach the tissues.
For the reason why this is permitted, see Shulchan Aruch HaRav (340:17) who explains that the Torah prohibition applies only to separating two items that are sewed together (which is done for the purpose of sewing them again), and not to tearing, and this is also the opinion of the Nishmas Adam (29:2).
Another explanation is that although all tearing, even that which does not involve mending, is rabbinically prohibited, it is permitted to tear where there is no possibility of mending (see Biur Halacha 314). Tearing a box to reach contents, in a destructive manner, does not involve any act of mending, and is therefore permitted.