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.
After pausing the search terms, it is also recommended to add negative keywords to a shared negative list and apply it across campaigns.
If it is absolutely necessary to remove search terms. go to the campaign detail view by clicking on the campaign, select the search terms from search term ad group button and click on remove button on top right.