One sheet, diffrent collaborators

This solution involves creating multiple reports.  But it will not require you to update multiple sheets regularly to provide new information to your collaborators.

You could create a report for each department and publish it.  Then send the link to each department. 

This will enable each department to see their information without having to share them to the sheet that houses all three departments information. 

The report will always be updated with saved changes from your origin sheet. 

Thanks,

Brandy 

Reports are a feature within Smartsheet and do not require a third party component or any additional costs if you are on a Team plan or higher. 

Reports pull information from other sheets to only show the information that you specify. But the information in a report will only be visible to collaborators who are shared to the sheet from which the information is being pulled.  You can publish a report and this will give access to those who are not shared to the "origin" sheet, since you do not want all departments to see into other departments these seems like the best option to me.  

If you do not care that departments can see each others tasks, but just don't want them to have to search for their own tasks, you can share everyone to the origin sheet and their report while specifying that you only want them to view their report for their tasks. This alleviates the need to publish the report.  

Here are some articles from Smartsheet on reports, sharing and sending reports, and publishing Smartsheet items to help better understand the functionality of this feature. 

https://help.smartsheet.com/articles/522214-creating-reports

https://help.smartsheet.com/articles/516096-sharing-sending-reports

https://help.smartsheet.com/articles/522078-publishing-smartsheet-items

Hope this helps.

Thanks,

Brandy