I'm not sure what the industry considers a "mini" vs just a "small" or "compact" excavator. My
local rental place has the baby bear starting at $1,000/wk, with the mamma bear version at $1140 and the papa bear at $1500. All are easily trailerable with a significant trailer and truck.
Do be sure your trailer and truck can pull it - if not be sure to budget the price of delivery and pickup.
In terms of "can it do it" - why yes, it can. I'm building a giant
hugel now with my little 21hp backhoe (
https://permies.com/t/146711/Building-hugel-Pond) and I know it would be faster with a tracked excavator. I've also seen significant
earthworks made with small excavators.
There is, as John poses, the question of "should you do it?" and ... that's up to you. A week seems like a long time to pull up some stumps and bushes, but building a hugel involves a lot of in-between time as you have to stage the logs, place the logs, compact the dirt - and I wouldn't want to pay someone to sit around while that goes on. And I wouldn't want to rush making the hugel either!