I'm working on no.9 of Leo Brouwer's 'Etudes Simples', and there are some pull-offs that I'm having difficulty doing cleanly; e.g. plucking an F# on the D string and an open G, then pulling off the F# to open D.

Any advice on doing this cleanly and without killing the other string?

Thanks, Natty D
How may The National D help you waste your time?
While you usually pull off downwards and you rest on the adjacent string, it doesn't apply in this case because you want the 3rd string to ring on. You just have to pull off outwards, insecure as it may seem.