"The mind of Europe" was a signifient term that emerged soon after the World War when T. S. Eliot defined it in an essay in 1919. By no means was he the creator of the actual concept, which can be traced back to the appearance of The Flowers of Evil by the French poet Charles Baudelaire in 1857.
It is interesting to note that Eliot's most significant contemporary in the Muslim world, Dr. Sir Muhammad Iqbal, defined "the spirit of Muslim culture" in his landmark poem 'The Mysteries of Selflessness' (1918) and later in the fifth lecture of his famous prose work, the Reconstruction (1920/34).
Both the "mind of Europe" and "the spirit of Muslim culture" have cosmopolitan outlooks. While Iqbal proclaimed that the Spirit of Muslim Culture was eager to enlist non-Muslims for the common cause of actualizing the oneness of humankind, the "mind of Europe" also seemed bend upon taking non-European adherents.
Clashes cannot happen between civilizations as such because each conflict is accompanied with mutually beneficial transfer of knowledge and fusion of cultures - even the proverbial Crusades were not devoid of such intermingling. It is also less likely that the spirit of one civilization could be at odds with the other. Therefore, perhaps the root cause of the present tension is that the Western academia for at least a century and a half has been defining its culture in terms of collective mind (whose extensions are collective consciousness, collective subconscious, and so on) whereas Islam could not define its own culture except with reference to "spirit" (whose extensions are collective self, consensus of opinions, and so on).
There is no clash of civilizations but yes, there seems to be a conflict between the mind of Europe and the spirit of Muslim culture.