when is the best time to cut tap roots on an evergreen to stunt the groth

What is your reason for doing this? Unless you want to bonzai the plant.

what plant, where's it growing

Sorry - missed the bit about it going into a miniature garden - need a new pair of reading glasses!

You didn't miss it, Cammomile, it wasn't there initially, it's been added. Geoban, trimming roots is a professional job, and not one I would attempt other than on plants like ivy or vinca, which put up with quite a lot of abuse. I'm not even sure you can trim the roots of conifers - you would be much better making your selection of plants for a miniature garden from dwarf conifers and other small versions of plants - the appendix 'nana' in a plant's name means it's small, so I recommend you choose more appropriate plants.