Siri works with HomeKit, SmartThings does not. However, there is a way to use HomeKit with SmartThings but it is very complicated, requires considerable technical skills, requires a separate device set up as a server, and if you were interested in that method you would probably be asking this question in a different way. But here’s the link to the video on that method if you are interested. Most people who are not already programmers won’t use it, though.
There is another much easier alternative, which is to use Siri to send a text message to the free IFTTT service and have that text message be the “if” in an IFTTT applet. This works fine, and it’s what we used to use before the Amazon echo came out, but there is a limit on the total number of messages you can use each month with the free service. It’s set, I believe, at 100 now, which might be enough for your use case or might not just depending on how often you were going to open the garage door.