To better understand SUSHI's performance in USD, we would need to normalize it with the crypto market, I've added a couple of tokens with large market cap such as WBTC (wrapped version of BTC), ETH, MATIC and DPI(Defi Pulse). DPI - https://indexcoop.com/defi-pulse-index-dpi

DPI is an interesting token that I've included in this analysis as an easy comparison with a broad base of established Ethereum based protocols. Projects included in DPI includes MKR, AAVE, REN, SNX, YEARN, COMP.

Looking at this graph, it does seems like there is a correlation between the price action of the SUSHI token and the price action of the large market caps. This can be seen when SUSHI and those tokens pump and the same time (eg. Apr'21 to May'21) and dumps at the same time in May'21.
However, there also seems to be an overall downwards trend in the price of SUSHI unlike the larger market caps coins.

Another way of understanding SUSHI's performance would be to look at tokens from similar DEXs which includes Uniswap (UNI), Balancer(BAL) and Curve (CRV). Balancer is a protocol similar to an index fund where one can provide liquidity up to 8 tokens and do swaps on. Curve is a stablecoin DEX with high liquidity and very low slippage as compared to usual DEXs.

Looking at the above chart, it does seems like the price action of SUSHI also correlates to the other coins, with amplitude varying across the tokens. In the largest dump in mid May, BAL had the largest drop of 63% followed by UNI (53%) and SUSHI (57%). For the overall trend over the past year, SUSHI had the largest drop of 69% followed by BAL (63%) and UNI (43%). Interestingly, Curve is the only one with an increase(33%).

Summary:

SUSHI price correlates highly to the overall crypto price action and BTC's price action. Given that BTC price action and market dominance largely correlates to how cryptocurrency performances, this is to expected.

In addition, the price correlation to other DEXs are also to be expected. Given their similar functions. One reason why UNI's drop in price is less severe than SUSHI is likely due to its continued development in swap technology such as Uniswap V3. BAL's drop is slightly less severe than SUSHI could be likely due to it's popularity in letting anyone create their own unique index fund where they can earn swap fees from. Lastly, CRV's price action is likely due to its rise in popularity in Curve Wars.