I was in the garden yesterday and noticed these vines/roots (not sure what they are)? They are in the same garden as my grape vine (I’m no gardener at all) and behind that garden bed too.

I’m stressing out as I did message my property manager (I rent) and she said that the vines can be removed so i started pulling some out and then went into full stress mode thinking I have killed the grape vine (Please tell me I haven’t!).

and here is a photo of the grape vine itself