Re: "Is there a spirit, from a non-religious point of view, as a separate thing from the mind?"
I would say yes, inasmuch as an emotional state, such as shock, is not the same as mind itself. But spirit is more that just a state. As the notes below show, it is also like a flame, and other things besides. It has a complex and intriguing origin.
The notes begin with two quotes from Jacques Derrida's essay, 'Of Spirit' (1987). As you will see, the meanings are generally quite down-to-earth, although they express the extraordinariness of emotional states -- spirited states, if you like.
The other angle, the burning flame analogy is interesting. You may have seen pictures of disciples with burning flames on their heads, or shining halos at least.
Image from Wikipedia

Jacques Derrida:
What is spirit?
The reply is inscribed in maxims which translate certain poetic statements by Trakl, in a form which one would call ontological if
ontology were still the dominant regime of these texts.
"Doch was ist der Geist?" Heidegger indeed asks. What is spirit? Reply: "Der Geist ist das Flammende." Further on, "Der Geist ist
Flamme."
How to translate? Spirit is what inflames? Rather, what inflames itself, setting itself on fire, setting fire to itself?
Spirit is flame. A flame which inflames, or which inflames itself:
both at once, the one and the other, the one the other. Con-flagration of the two in the very con-flagration.
(Of Spirit, page 84)
Martin Heidegger (translated by J. Derrida):
The burning up is the radiance of a reddening glare. What burns
itself up is Being-outside-itself (das Ausser-sich) which illuminates
and makes shine, which also, however (indessen auch), can devour
tirelessly and consume everything up to and including the white of
the ash (in das Weisse der Asche verzehren kann).
"The flame is the brother of the palest" is what we read in the poem Verwandlung des Bösen (Transmutation of the Evil One). Trakl
envisages "spirit" on the basis of this essence which is named in
the originary meaning (in der ursprünglichen Bedeutung) of the word
"Geist," for gheis means: to be thrown (aufgebracht), transported [or
transposed, deported: entsetzt, again -- and I believe this is the
most determining predicate], outside itself (ausser sich).
(Of Spirit, page 98)
---------<<<{{O}}>>>---------
... spirit was initially used to translate Greek pneuma and
Hebrew ruah, starting in about 1250, and all versions of the Bible
from Wyclif onward use spirit in translation of the Greek and
Hebrew. Prior to the Middle Ages, however, ghost was used. It
comes from the Indo-European root gheis- "fear or amazement", and
there are descendants of that root in most of the Germanic languages,
all of them possessing similar meanings. Some etymologists believe
that Sanskrit he'das "anger" is related, and the general meaning
of related words outside of the Germanic language family appears to
have been "fury, anger".
http://www.takeourword.com/Issue082.html
Geist. m. Old and Middle High German geist, Old Saxon gêst from West
Germanic *gaista- m.: "supernatural character or being, emotional
state;" also in Old English gâst, Old Frisian jêst. From the
Indo-European root *gheis-d- : "to be out of one's mind" [au er sich
sein], also in Sanskrit hîd-: "to be angry" [zürnen]; unexpanded in
Avestan zaêsa-: "terrible, dreadful" [schauderhaft], Gothic
usgeinan: "to be frightened" and usgaisjan: "to frighten"
[erschrecken], Old Norse geiskafullr: "completely frightened." To the
extensive family of
*ghe/ghei- : "yawn" [gähnen], belongs also the sense "to open wide one's mouth", hence probably a derived root *gheies-: "Wide opening
of the mouth"; the -d- is probably a short grade of *dô-: "to give."
Therefore *gheis-d- would mean: "to bring about a wide opening of the
mouth" [Mundaufsperrung herbeiführen]; "to make someone open his
mouth wide."
http://www.albany.edu/offcourse/july99/hache.html
In regard to Beowulf:
Gæst occurs 8 times apparently meaning "ghost," or "demon" only, as a
masculine noun, with variations of 4 compound nouns ('ellen-, ellor-,
geoscaft-, and wæl-'). At least two instances are uncertain. Gæst
(also spelled gist,) occurs 9 times, with the apparent primary
meaning of "guest." Lexicographers from Bosworth and Toller onwards
have differentiated in their editing of instances of this word or
words, according to whether they see Grendel and his Mother as
demonic. ... A more recent editor suggests that only context can
decide. The difference is important because the words seem to
distinguish between the natural and the demonic, accentuating
Grendel's and his Mother's monstrous natures. The American Heritage
Dictionary of Indo-European Roots notes that gæst meaning "guest"
derives from *ghos-ti, meaning "stranger, guest, host," and "someone
with whom one has reciprocal duties of hospitality." Reflexes of the
word include Germanic *gastiz, Latin hostis "enemy" and Greek xenos,
"stranger." Lewis and Short note that Latin word hostis, derives from
the Sanskrit root *ghas- to eat, consume, or destroy" and that the
Germanic gast is derived from the same word. The compound of this
word in Latin, hospes, adds the suffix "pa" "to feed," thus combining
the idea of feeding with the word for stranger, and then contracting
to "hospites" or "he who entertains a stranger." The American
Heritage Dictionary of Indo-European Roots gives gist as deriving
from
*gheis in an unclear original meaning, having to do with "fear or amazement," with the "suffixed o- grade form *ghois-do in Germanic
*gaistaz, a ghost." The Oxford English Dictionary notes that word's etymological relations are "fury, anger.... the root "*gheis-,
*ghois- appears with cognate sense in ON geisa to rage, Gothic usgaisjan to terrify; outside Teutonic the derivatives seem to point
to a primary sense "to wound, tear, pull to pieces." This last may
suggest a link between the two original words, since both roots have
to do with consumption, with a possible development from the
relatively neutral *ghas- , "to consume", to the more negative
*gheis-, "fear." The first would note what is expected from a social relationship, the offering and consumption of food, while the second
would encompass the possible excesses of a guest who destroys.
Simple, ritualized consumption gives way to destruction and
fragmentation. The negative association of the supernatural world
with cases of excess would also make sense, in that enforcement and
punishment of those who break the treaties is projected into the
realm of the gods, as numerous examples in Greek demonstrate. The
case for reading the disputed words in Beowulf as either "guest" or
as "ghost," or as reflexes of the same idea, cannot be solved here,
since there is no syntactical or prosodic reason to prefer one to the
other.
http://www.mun.ca/mst/heroicage/issues/5/Anderson1.html