I am pretty superstitious and plan everything I do with my plants according to the Lunar Cycle and harvesting is undertaken when there is a "waning" moon, which is the two weeks between the Full Moon and the New Moon. Apart from thanking Mother Nature for the opportunity to, like you say, have the privilege of enjoying these beautiful plants for a period of time before killing them, I just thank the "Plant Gods" and ask for forgiveness at taking a life.
I am not sure about specific Native rites/rituals, which would be interesting to research, but console myself with my own little ritual I have developed for the situation of ending my plants life. I also like to think the plant is happy for me to do so, so she can show me how "special" my care has made her and that she would like to reward me for all the love and care I had invested in her.
Hope this helps,...... Organoman.