depends on the plant or tree your doing it too as some heal a lot better than others . also some plants bleed like grapevines if cut at the wrong time . id do trees early spring too give them a better chance of healing .

mmm mabye even winter since they dormant,in spring they start growing leaves and it is a huge shock for them cutting the branches off.

If you go for early spring do it before the sap starts rising. It used to be recommended that you treat the cut surfaces with Arbrex but its now thought not to be necessary. Silver birch is the worst for dripping sap.
Something tough like sycamore doesn't seem to care what you do. Its always a help with this sort of question to know which tree and how mature or otherwise it is.

Thanks for your comments, I should have stated that its a monkey puzzle tree

Sorry I've no experience of those. If in doubt go for winter.

I ment before the sap rises sorry if I was unclear .