Both "dissociate" and "disassociate" are defined as removing an association but is there a difference between the two? Does the "associate" part of "disassociate" imply a stronger former connection missing in "dissociate?"
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OED says disassociate dates from 1603, and dissociate from 1623, so neither is meaningfully "the original". They're basically the same word, but if you believe this NGram dissociate is used more commonly by a factor of about 4:1 in total.
Many instances of disassociate will in any case be for the specialised chemical sense (compounds breaking down into atoms, ions, etc.) which only applies to that form, so for OP's meaning the usage figures are even more skewed.
Merriam-Webster's dictionary of English usage implies that apart from where that difference in meaning applies, you should probably prefer the shorter word - partly because it is shorter, and partly because it's the more common form. There are no other considerations, or differences in use or nuance.
I understand that the dictionary definitions are the same. I think dissociate makes sense in most situations, as in the chemistry examples given, and in psychiatric definitions (Dissociative Identity Disorder), mostly because of existing convention and brevity. But as for things that were intentionally or manually associated in the first place, disassociate seems more natural to me, whether or not it is indeed any more correct. For example, in my field of Information Technology, we tend to say disassociate when breaking a logical connection between elements or constructs that we ourselves had associated in the first place - at least among my colleagues here in the U.S.