The MP Select Mini uses a Right Hand MK8 Extruder. A few acceptable replacements are listed below. Some listings will have a choice of left or right hand model. Be sure to choose “right” or “right hand”.
Watch Thomas Sanladerer calibrate his extruder.
GigDigit - Extruder - Feed Mechanism for MP Select Mini V1, V2, Pro/V3
GigDigit - Extruder Gear
(Be sure to verify the one you need matches the product pictures as there have been two types used)
GigDigit - Bowden Connector for New Type Extruder / Feeder Mechanism
GigDigit - Bowden Coupling / Connector - PC4-M6
Amazon.com - Redrex Right Hand 1.75mm Filament MK8 Bowden Extruder
Amazon.com - Anycubic All Metal Right Hand MK8 Extruder (Gold Color)
NOTE: Requires two M3x20mm screws or two M3x25mm screws and maybe a couple of M3 washers that are not included.
eBay.com - 3D Printer MK8 1.75mm Filament Aluminum Alloy Extruder Kit W/ Bracket (Black & Red)
NOTE: This is optional but if you would like to keep the original/stock extruder gear, you will want to also purchase a 4x10x4mm bearing (examples linked below). The benefit is that you won't have to struggle to remove the existing gear and you won't have to recalibrate the extruder. Removing the existing gear can be troublesome but applying heat to the gear with a heat gun, lighter, small torch, or similar should make the task a little easier due to the thermal expansion of the gear. This should go without saying but please use a tool or something other than your hands to grasp the gear after heating.
McMaster-Carr - Stainless Steel Ball Bearing - Premium Double Shielded, for 4mm Shaft Diameter, 10mm OD