I don't know why you've titled the difference as being about "mysticism". To put it simply, Marx is not a very good interpreter of Hegel (for the take of another Hegel scholar see Dudley Knowles, Routledge Guide to Hegel and the Philosophy of Right , p. 20). So Marx critiques what turns out to be a fundamental feature of Hegel's philosophy which demonstrates how badly he's misunderstood the dialectic.
For Hegel, there are three different approaches to truth: art, religion, and philosophy. Skipping over quite a bit of the Phenomenology and moving towards the ending, what turns out to be the case is that each of these three can give access to that which is in and of itself (i.e. Truth) and the means through which truth is accessible is either through imagery (art), through faith (religion), or through knowledge (philosophy). In other words, ideal art is right about what it represents, ideal religion is right about what it believes, and ideal philosophy is right about what it comprehends.This sort of triadic structure is common in Hegel's philosophy and is called dialectic. There's actually multiple forms in the text itself (but we needn't understand that to understand this point). The think that engages in all of this is for Hegel Geist -- rendered in English classically as "Spirit" and more recently as "Mind". Thus for Hegel, religion and thinking of God is not wrong but is second to philosophy.
What causes Marx to disagree with this account? Marx wants to keep a dialectic but does not understand humans as thinkers. Instead, he views the dynamic in terms of capital and how it causes relationships. Thus, his view is called dialectical materialism -- whereas Hegel is dialectical but not a materialist.
Where this matters for the case of slavery is in Hegel's classic Master-Slave dialectic (probably better rendered as "lordship and bondage"). It's a commonly referenced but misunderstood passage and subject to multiple interpretations. On the simplest level, Hegel is making the following points:
(1) the master does control the slave physically
(2) but "master" and "slave" are social identities
(3) the "slave" is made a slave by the master's consciousness and subjugation of the person socially.
(4) thus, the master ultimately depends on the slave for recognition as a master as well.
Hegel's point is that while the master controls the slave "master" and "slave" are identities that are mutually dependent on recognition. (Hegel will later draw this into society by pointing out that the identities of selves depend on each other and society). Thus, for Hegel, the slave can be freer than the master in terms of Spirit because the slave's thoughts are free whereas the master's body is free.
Marx's dialectic does not engage in terms of "Spirit" (i.e. consciousness), so he just sees that the master is getting more use out of the slave than vice-versa on a material level.