How do I learn-by-practicing digital circuits - MIPS R2000 (or similar) processor or board?
I think you have some misconceptions about how dev kits work. A dev kit for a certain processor architecture isn't a tool for developing a new or similar processor, it's for designing a system that includes the said processor (or another member of its architecture family). 

Now, if you want to learn how a processor works internally, there are some basics you need to cover first. I often point to https://www.nand2tetris.org when people ask me about where to start. This course introduces many important concepts of digital design. It even includes a simple Hardware Description Language or HDL that you use for designing (and simulating) everything from simple logic gates to your own CPU and computer system.

If you want to design and test your own logic circuits, there are basically two options. Either you get a breadboard and some number of 74-series ICs and discrete components (resistors, caps, etc.) to experiment with, or you get an FPGA board that lets you program your logic circuits onto an FPGA. I don't really work with FPGAs, but people tell me this is a good starting point: https://www.nandland.com

Actually designing and producing your own CPU chip is a very complex (and expensive) process, that requires a lot of knowledge about semiconductors physics, lithography, production processes, etc.  

If you really want to design and test your own CPU, an FPGA is your best and affordable option.

Finally, designing and producing PCBs is a whole topic on its own. There are a lot of things to consider before and during the design of a PCB, here is a simple introduction: https://www.edn.com/design/pc-board/4424239/PCB-design-basics

If you get yourself a good breadboard and/or FPGA board for experimenting, you should be able to get a long way along before you need an actual custom PCB. There are people who build whole simple computers on breadboards. It will also keep your costs down since you'll only need a few tools like a standard soldering iron, a multimeter, pliers, etc.

So, the tl:dr version:


Learn the basics of digital design (boolean algebra, basic circuit analysis, etc.)
Experiment with basic logic gates like NOT, OR, etc. 
Build simple advanced components like latches and flip-flops 
Keep improving them into registers, ALU, etc. until you have all components for a simple CPU
Verify your CPU design with the help of an FPGA and/or an HDL like VHDL or SystemVerilog.