Mining station vs. mining colony
Minor frame challenge: why a mining colony on the surface? To my knowledge, the approximately $\frac{1}{445}$ of a G of gravity on Pasiphaë's surface does essentially nothing useful or detrimental, whereas if you place a mining space station in a quasi-satellite orbit of Pasiphaë — that is, with the same semi-major axis, inclination, and ascending and descending nodes, ahead of or behind Pasiphaë on its orbital track — it also stays in a constant position and is less prone to solar eclipses. It will still be very easy to get to Pasiphaë's surface from such a colony, given Pasiphaë's escape velocity of approximately 36 m/s (which will fall as it gets mined away), and it won't fall inwards at any point. 36 m/s is almost always (like, 99.999% of the time, exceptions exist) too high a speed for a human to survive uninjured but not too hard to get around with jetpacks or very light rockets, likely low-impulse monopropellant ones — like, Lunar Escape System-level barebones. Hell, maybe a couple of really powerful fire extinguishers strapped together if it's an emergency.
Provided the mining colony must be on Pasiphaë's surface, however, the answer to this question can be one of two things.
From the inside out
Let's assume miners dig all the way to the core, or close to the core, then hollow it out from there. If they're doing a network of criss-crossing tunnels across the insides I can't really model that.
This excellent Astronomy Stack Exchange answer provides the total downward pressure applied by gravity to a hollow shell, because, like you, many people are apparently interested in hollowing out astronomical bodies:
$$\frac{11\pi G \rho}{8}R^2$$
wherein $G$ is the gravitational constant, $\rho$ is the density of the shell, and $R$ is the radius of the shell. Plugging in 2.9$\frac{g}{cm^{3}}$ for density (sources conflict between 2.6 and 2.9$\frac{g}{cm^{3}}$) and 30 kilometers for radius gets about 752 pascals of downwards pressure (as opposed to the 2.9 megapascals of the hypothetical hollow moon in the linked example). This represents a net pressure of $(\pi/8) R^2 P dr$ wherein $R$ is the radius of the overall thing, $P$ is the pressure figure, and $dr$ is the derivative of the shell's thickness (i.e. a dimensionless number equal to the shell's thickness in km). This is then divided over an area of $A = \pi W dr$, wherein $W$ is the radius of the hollow section and $dr$ is another derivative of the thickness of the shell, to find the downwards pressure across the inside of the shell.
Plugging in values of $R$ = 30 km, $P$ = 752 pascals, $dr$ = 29.9 (representing a shell thickness of 29.9 kilometers), and $W$ = 0.1 (representing a hollow area 200 meters across) gets me a pressure figure of about 8.46 megapascals, which is not an unreasonable level of pressure for rock to withstand. This math breaks down the closer you get to the center, with the pressure asymptotically approaching infinity, but provides a roughly accurate indicator of roughly how small a hollow sphere around the core can be without causing a collapse.
In other words, this means the hollow area in the middle can be as small as 200 meters across, and potentially somewhat smaller depending on rock compressive strength, without the outer layers collapsing onto it. The larger that radius gets, the greater the ratio of rock strength to downwards force; if Pasiphaë is reduced to a shell 100 meters thick with a hollow sphere 29.9 kilometers in radius within, the downwards pressure on that sphere is only ~95 pascals, although at that point imperfections in the rock likely mean it'll crack and break up into a debris field. The image of a thin little Pasiphaë-shaped balloon of rock where a moon once stood, pretending to be it while actually being hollow, is amusing but unfortunately impossible.
To sum this up: if you want to mine it from the inside out, mine down to about half a kilometer from the center, for safety's sake, and then mine out a hollow shell between the outer shell and an inner sphere surrounding the core. The shell will be too strong for gravity to collapse it (and it will get stronger the further out you mine) while the sphere around the core can be mined out once the shell has been disconnected from it.
Note that all these values depend on what you plug into the equations, but the general concepts should remain the same. For instance, if it turns out Pasiphaë is a little less dense, that reduces downwards pressure somewhat but implies some of it might be made of water ice, meaning lower compressive strength, meaning maybe you want to mine down to two kilometers away from the core instead of half a kilometer or somesuch.
If you're wondering why this can't be done with larger objects: they have hot cores that kill your miners and drills. I'm pretty sure a body has to be about the size of 4 Vesta to do that kind of thing with rock and metal; Vesta is internally differentiated which means that there's enough heat to melt its guts and rearrange them. Pasiphaë is nowhere close to large enough for that, as far as I'm aware, although it might be warm enough on the inside for volatiles to do something similar.
From the outside in
If you mine from the outside in (strip mining, so to speak), things become significantly easier, simpler, and less mathematical. In this case, think of Pasiphaë as a dog with a tick (the mining colony) attached to it, rather than thinking of the mining colony as sitting on Pasiphaë.
In this case you simply mine Pasiphaë from the outside down/in, layer by layer, until you have the mining colony sitting atop a 30-kilometer deep wedge of rock. Then you just mine the wedge of rock, starting from the side opposite the mining colony and ending at it.
In all cases, the answer is the same: the entire thing. You can mine the entire moon into nonexistence.
However long that takes you depends on the rate at which you mine it.
Perhaps there's a ceremony for when the last chunk of Pasiphaë is hauled into the mining station and processed. Maybe the last couple hundred tons are broken up and sold as souvenirs: "look, Ma, I have a piece of a long-dead moon!"
