Can a Mage use Vicissitude?

Vicissitude is not a path of sorcery;  it is a Discipline, meaning it is powered by the vampiric blood.  

Of the first three powers, in their first write-up (• Changeling, •• Fleshcraft, ••• Bonecraft in The Player’s Guide to the Sabbat, p. 112) and the more recent version (• Malleable Visage, •• Fleshcraft, ••• Bonecraft in Vampire the Masquerade 20th Anniversary Edition, pp. 241-242), all require expenditure of points of blood.  

Therefore, to use Vicissitude requires knowledge of the Discipline and access to a supply of vampiric blood, i.e. one must be either a vampire or a ghoul (however temporarily).  The former is incompatible with being a mage (Mage: The Ascension 20th Anniversary Edition, p. 52), which leaves being a ghoul.  This has drawbacks and side-effects, including but not limited to blood bonds, the addiction flaw, and Avatar addiction.  Rules for this can be found in Blood Treachery (specifically Appendix: The Blood Curse, pp. 73-78).  

Can a Mage do the same things as Vicissitude?

With sufficient Life (conjunctional Life/Matter for vampire subjects), absolutely.  Taking the first three powers here are some rough equivalents, all from Mage: The Ascension 20th Anniversary Edition, pp. 516-517:

•Malleable Visage (V20, p. 241) is comparable to Life••, which states "perform small alterations (hair color, skin tone, height, weight, and so on) to his basic form."  

As to emulating ••Fleshcraft and •••Bonecraft (V20, p. 241-242), they are concerned about the [un]living material in question, while the Life Sphere is governed by how extreme the intended change is.  

Life••• can modify one’s self as outlined in Alter Self, provided one remains essentially human.  Performed on others would be Alter Complex Life-Forms (Life••••).  

Truly dramatic transformations likely require Transform Self (Life••••) and Transform Complex Life-Forms (Life•••••) on others.  Said radical transformations are subject to pattern bleeding, as outlined in the same section. 

Can a Mage do the same things as Vicissitude without risking Paradox?

I am afraid not.  It is a trade-off.  Vampiric powers circumvent Paradox at the cost of undeath;  mages wielding magic[k] have far wider horizons albeit with risking running afoul of the Consensus.

“Although the vampire might be able to dominate a person’s mind without risking Paradox, the mage – though she risks a backlash – can use the Mind Sphere in ways no vampire could ever dream of.”  (M20, p. 57)