How can I stop my existing SIP in a mutual fund without selling the units?

Stopping your SIP is not the same as selling your units. Even when you stop your SIP. Your existing units will continue to appreciate the scheme till you redeem it. The procedure for stopping your SIP with each individual broker is different. In this case, you can just call the brokerage house and request them to cancel your SIP.

Alternatively, you can also go to the website of the AMC and create a login id and password with your folio no, mobile no, and email id. On the website, you have the option of stopping SIP. Else, you can also fill a STOP SIP form with your AMC and sent it across to the 1 month before your next SIP is due.