How to cut this tree back?

It’s my first spring in this house, and this tree/bush is getting a bit big for its space. According to my app, I think it’s a New Zealand Broadleaf (Griselinia Litroralis??)

There were branches and leaves basically all the way to the ground, but I’ve cut them back and cleared the debris. However I’m worried it starts to look like a mushroom if I continue.

Also unsure how to go on with all the wooden branches inside the tree. If I cut back into the woody stuff will it green up again?

 

Its often grown as a hedge but capable of reaching 8mtrs high(2 storey house inc roof ! ) What is visible behind it if you remove/prune severely?
Shrubs: pruning evergreens / RHS
RHS pruning advice
If it were mine, and the vista behind it was not ugly, then I would look to get it reduced in height to 2 metres or so. If it is cut back to this height at the centre, the outer branches will grow new growth to fill the light. This gives the opportunity to progressively shape it so as to correct its form and take up less space.
Alternative would be to remove completely, returning you a considerable area to do with whatever you prefer. How does it fit in your dreams ?

 

@infradig thank you for your advice.

It’s just the garden fence behind it, however I think the fence might be relying on the tree to keep it up!
I don’t want to lose it as it gets lots of birds visiting.

I’ll look to keep its height in check as you advise.
Thanks

 

I’ve just reduced one of my Griselinias from eight foot to three foot @Novice Gardener Laura. They bounce back quickly. I have two hedges of them and several single plants grown as columns or unshaped. They are very versatile and forgiving if they like your soil and climate .

Now is a good time to prune before fresh growth begins. Removing the lower branches as you have done is a good way to allow light in for any plants growing below. Just take your time, looking at it from different angles as you work until you get the shape you want. Don’t worry if you take too much off, it will soon grow back.