Artifact archival takes in a pattern for matching target files. Similarly, it also takes in a pattern (ANT build system pattern for matching files) for exclusion as well which will be ignored while selecting the files for archival.
For e.g.
archiveArtifacts artifacts: 'output/*.txt', excludes: 'output/specific_file.txt'
The above command will archive all the text files from the output folder except specific_file.txt