Normally, you need a
TN for ANY work you do on US soil.
However, if the client you are working for while in US does not have any US affiliations, and is not benefitting from your presence in US, then you can do work for them. The country that the client is in is immaterial, and so is your Cdn citizenship. That would only come into play if you were working IN Canada.
You would want to check with a US immig lawyer (and your clients) to be sure that no US affiliate is being grieved by your US-based work without authorization.
As to taxes, since it is work being done as a contractor while in US, it is not taxable in Canada, by treaty. You report it on your 1040 as self-employment income. Your Cdn clients might withhold Cdn
taxes under Cdn rules, but you would get those back by filing a Cdn return, reporting no income, and citing the treaty.