Which library to use for 23LC1024 SRAM 1 Mbit
SPI RAM has two modes of operation: single byte and "page mode".

In single-byte mode you first send the read or write command followed by the (typically 3-byte) address and then read a byte. That's 5 bytes per transaction, or 40 SPI clock cycles. At the maximum of 8MHz (SPI_CLOCK_DIV2 on a 16MHz MCU) that would be at absolute best (1/8000000*40) 5µS per byte read or written. That's not including the time taken to toggle the CS pin and perform the other software-level parts of controlling the SPI peripheral.

In page mode it is possible to send one start address and then read or write sequential data from that address upwards. Ideal if you need to read a larger number of bytes that are sequentially in memory. For instance, to read 100 bytes sequentially it would take 104 SPI bytes - one for the read/write command, three for the start address, and 100 for the data. That is 832 SPI clocks, or at 8MHz, 104µS. 

As you can see, reading 100 bytes within 10µS is not possible on an Arduino with SPI SRAM. There just isn't enough speed. Even 100 sequential bytes. 100 "small groups of bytes" just ain't gonna happen. 

There are other technologies that are faster which may be more suited to your use, but they require different peripherals in the chip (namely SQI), and the chips with that in tend to be more powerful and have more RAM anyway, so your 1Mb of external SRAM would be redundant.