Por favor de no cortar estos arbustos. Nos gusta en su estado natural.

Yes, "por favor de", although it maybe used coloquially is not correct. "Haz el favor de, Haced el favor de, Hagan el favor de..." could be another correct option for your sentence.

Ah, thank you! I'm sure Becky is quite good at Spanish, but I didn't notice she was not a native until now.

"Por favor de" sounds reaaaaally off to me. I don't think it's good Spanish. I'd say: "Por favor, no corten estos arbustos: nos gustan en su estado natural".