Will macOS Mojave 10.14 slow down an early 2011 13" MacBook Pro?
As Nimesh already noted in his answer, that MacBook Pro is no longer supported.

But as chriszanf commented: "Machines outside of those spec can be upgraded using dosdude's app: dosdude1.com/mojave" 

But apart from being unsupported that brings another caveat. Just installing that will work, but is no fine experience at all. For once, the installer will convert your magnetic drive HDD from HFSplus to APFS, and the new filesystem is a terrible performer in general and even much worse on rotational disks. That will slow you down.

Using APFS on hdds and why you might not want to

You also have to keep in mind that your graphics card is not exchangeable and does not supported Metal. That will slow you down.

The problems do not end there. And the list of hacks and workarounds you might have to hunt down is also long. 

It is possible to install it. But probably not really worth it. 

If you have some time on your hand, the following thread lists some experiences in attempting this:

macOS 10.14 Mojave on Unsupported Macs Thread and it is very conveniently just 471 pages long by now.

Personal commentary: on that hardware 10.12 Sierra is the last "known good" performer for me. That is currently at least also updated with security patches.