the GPU I plan to get is a Zotac GTX 1070 Mini but the pcie slot is pretty low, the distance between the slot and the bottom of the case is about 3.5 inches
You can check the website for your case. It should list the supported graphics card dimensions. Otherwise you can measure the area for the GPU. Measure the length from the external expansion slot along the PCI Express x 16 slot to the nearest case obstruction (length). Do the same from the top of the PCI Express x 16 slot on the motherboard to the nearest case obstruction (height). Then compare those dimensions to your graphics card.
You can check the website for your case. It should list the supported graphics card dimensions. Otherwise you can measure the area for the GPU. Measure the length from the external expansion slot along the PCI Express x 16 slot to the nearest case obstruction (length). Do the same from the top of the PCI Express x 16 slot on the motherboard to the nearest case obstruction (height). Then compare those dimensions to your graphics card.
the GPU I plan to get is a Zotac GTX 1070 Mini but the pcie slot is pretty low, the distance between the slot and the bottom of the case is about 3.5 inches
The card you linked will work just fine and it really should have plenty of clearance but like was mentioned, you may need to check your power supply to be sure that it can supply enough clean power.