Clockwork prosthetics should be affected by magic suppression the same way constructs are, and necrograft arms and legs should be affected by magic suppression the same way undead are. Which is to say,
[Antimagic field] has no effect on golems and other constructs that are imbued with magic during their creation process and are thereafter self-supporting (unless they have been summoned, in which case they are treated like any other summoned creatures). Elementals, undead, and outsider are likewise unaffected unless summoned. These creatures’ spell-like or supernatural abilities may be temporarily nullified by the field.
So the graft itself is not affected; a clockwork or necrograft arm continues to function as an arm, at the very least.
As for their special abilities, if those are magical they would be suppressed by antimagic field or dispel magic the same way the spell-like or supernatural abilities of constructs or undead would be. However, most of them seem very much physical functions of the graft. Clockwork arms and legs allow you to lift more, because they are stronger. Undead flesh is often tougher and doesn’t tire, hence the advantages of the arms, legs, and sallowflesh. The strangler’s tongue comes from a mohrg, whose paralysis ability is probably Extraordinary (though it does not actually say, supernatural paralysis is usually explicitly marked as Su; see the lich’s paralyzing touch for example). Even the enhancement bonuses provided by several of the necrografts seem to me to be non-magical in nature: nothing about enhancement bonuses says they must be magical (though they usually are), and the explanation for why they impart these bonuses are all very physical.
Really, the only two I find questionable here are the ghoulgut and gravegland necrografts. These provide more active effects, which could conceivably be separate magic effects suppressed by antimagic field or dispel magic. The ghoulgut still seems pretty physical to me, but I can buy it being magical. The gravegland is even more apparently magical; I could accept an undead organ having non-magical access to negative energy, but it is a stretch. I’d probably allow it if I were GM, but wouldn’t expect others to.
Finally, I would point out that these grafts’ antecedents in 3.5 were more detailed. Grafts appeared first in Fiend Folio, and were also found in Libris Mortis, Lords of Madness, Races of the Dragon, Faiths of Eberron, and Magic of Eberron. These have many more rules, as well as many more grafts, which may be useful to port to these Pathfinder options. In fact, these books actually present two different types of graft: the “old” style in Fiend Folio, Libris Mortis, and Lords of Madness, and the “new” style in Races of the Dragon and Eberron. These differ in a variety of ways, so I leave investigating how or whether you want to use one or both in Pathfinder as an exercise to the reader, but of relevance to this question, both styles explicitly state that the graft, once applied, functions in its entirety even without magic.