We always advice our users to pause irrelevant search terms and not remove them. By pausing the search terms, you ensure negative keywords are present in other ad groups to avoid the ad to be triggered.
for eg: in a scenario of 2 search terms adwords software and free adwords software. Instead of removing free adwords software it is recommended to pause it. This will ensure free as a keyword will be negative in adwords software ad groups thereby avoiding any irrelevant search to be triggered from that ad group.
Please note pausing ad groups will not add it in the shared negative list. After pausing the search terms, it is also recommended to add negative keywords to a shared negative list and apply it across campaigns. For example in the above case you do not want to show ads for free related keywords. When you pause the search term 'free adwords software', any search query related to this keyword (in all exact, phrase and broad matches) will not trigger ads. However in future, since we detect new search terms during maintenance and add them to the campaign, we might add a keyword saying 'free adwords tool'. This is a keyword which you do not want to advertise for. So its better if you add 'free' in the negative list to never trigger ads for such keywords. You should add 'free' as a broad negative keyword in the list and apply to the campaign. Learn more about adding negative keyword lists here.
Please note the system will not create any child keywords of 'free adwords software' since you have paused it.