Where it's whole projects that I pause, it's quite easy to set the project to suspended and then change my view filter (or grouping) to hide all the tasks in that project. For individual tasks, this will take quite a lot more clicks and time to manage. There are a few options:
I often adjust the start and due times to defer a task to when I next need to start it and the deadline (not the anticipated date) when it's got to be completed. For me start time can be dynamic and doesn't need to be left at the date I first started the task. The advantage of changing start date is that you could set up your filter so that the task comes back on the list later on and you don't completely forget about it.
Alternatively, you could use a flag to tag tasks which have been paused.
Another option would be to set the urgency or the importance to minimum, for those tasks you can defer.
Just a few options, there. I'm sure there are many other ways to use categories or other task properties, in combination with a filter, to temporarily hide tasks.