I don't have any problems with Yosemite and EOS utility...have you downloaded the latest version from the Canon website?...some of the bodies (eg canon 7D2) don't say their software is compatible with Yosemite, however just use the Maverick download.
If you said which Canon body and version of OSX you are using, perhaps I can post a link.
You haven't said which version of Mac OSX....that would be helpful!
Have you just got the camera and installed the software that came with it or did you have a previous Canon camera and are using the EOS utility for that?
You obviously have a version of Canon EOS utility installed on your Mac, so updating that won't be a problem, so if you follow the links below it should all work fine.
To get the latest software, visit the following site
Go to "drivers and software" and if you are on yosemite, it will tell you that Yosemite is not supported, so click on the operating system options to the right of the box and select "Mavericks" and it will let you download the appropriate software, always assuming you are on either Maverics or Yosemite.
Once it has downloaded, just open the file and install it, it will overwrite the old files and should then recognise your camera.
Hope that helps,
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM