It's my impression, from a distance, that the sentiment in Scotland is anti-Brexit, and is in favor of remaining with the EU. That would seem to cloud the issue of whether this is a "separatist" movement.
It's definitely a separatist movement, although it does come across as a loaded term.
Scotland was resoundingly anti-brexit. This situation is worsened given the 2014 vote against independence was decided at least in part around arguments that leaving the U.K. would mean leaving the EU - for a subsequent vote to remain to be essentially ignored as a result of a UK wide referendum has likely done little to reassure Scotland that Westminster takes it seriously.